env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ○, the rules are as follows:
when x is odd, x ○ y = x ** y + x - x;
otherwise, x ○ y = y * x / x - x + x.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expressio... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x + x - y。
和 ▽，规则如下：
当x和y都是奇数时，x ▽ y = y - x + y；
其他情况下，x ▽ y = y + y * x。
和 △，规则如下：
实数域上，x △ y = y ▽ x * x。
运算优先级：⊗ > ** = ▽ = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ▽ 9 ⊗ 2 △ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "46080",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 9 ⊗ 2 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ○, the rules are as follows:
when x is odd, x ○ y = y / x - 4;
otherwise, x ○ y = (x - y - x).
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 ** 5 ○... | {
"game_data": {
"answer": "-7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ** 5 ○ 6 - 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ⊙, the rules are as follows:
when x is odd, x ⊙ y = x + x + y;
otherwise, x ⊙ y = x + y - x.
and ◎, the rules are as follows:
when x is a multiple of 3, x ◎ y = y * x + x;
otherwise, x ◎ y = y + x + x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + (3 + y).
The precedence of ope... | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◎ 4 ⊙ 3 ⊕ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y * x - x。
和 ◎，规则如下：
当x等于y时，x ◎ y = y - (y) * x；
其他情况下，x ◎ y = y - x / y / y。
和 ⊕，规则如下：
当y是奇数时，x ⊕ y = 1 / (x + y) ⊙ y；
其他情况下，x ⊕ y = y * 5 * 1 - x。
运算优先级：⊙ = ◎ > ** = ⊕ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 / 3 ◎ 7 ⊕ 5 / 3 ⊙ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.029529",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 / 3 ◎ 7 ⊕ 5 / 3 ⊙ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y / x - x。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ♢，规则如下：
当x大于y时，x ♢ y = x + y；
其他情况下，x ♢ y = (5 * y - x + x)。
和 ☆，规则如下：
当x和y都是奇数时，x ☆ y = y - y ♢ 4 / x；
其他情况下，x ☆ y = y - x ♢ x * y。
和 ⊗，规则如下：
实数域上，x ⊗ y = 2 / x - 4 / y。
运算优先级：** = ♢ = ⊗ > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ⊗ 9 ☆ 3 ♢ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.555556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊗ 9 ☆ 3 ♢ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define ○, the rules are as follows:
when x and y are both odd, x ○ y = abs(y * x);
otherwise, x ○ y = abs(x - x - y).
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expr... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ☆，规则如下：
当x是偶数时，x ☆ y = y + y + x * x；
其他情况下，x ☆ y = y / y + x。
和 ▽，规则如下：
当y是5的倍数时，x ▽ y = y / y - y - x；
其他情况下，x ▽ y = x * y * x。
运算优先级：▽ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ☆ 2 ▽ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "40",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 2 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x * y - y。
和 ⊙，规则如下：
当x和y的和是偶数时，x ⊙ y = y - y - x；
其他情况下，x ⊙ y = x * y - x。
运算优先级：□ > ** > * = / = % = ⊙ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 / 4 □ 3 + 4 ⊙ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-3.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 / 4 □ 3 + 4 ⊙ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y + (x - x + x) - y.
and △, the rules are as follows:
when x is a multiple of 5, x △ y = y + y - y * x ♡ x;
otherwise, x △ y = x / x ** y + 2.
The precedence of operations: ♡ > ** = △ > * = / = % > + = -。
Parentheses have the highest priority, ... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = y - abs(x - x * y);
otherwise, x ▽ y = abs(x + y).
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the ... | {
"game_data": {
"answer": "4.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 5 ▽ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y ** x.
and △, the rules are as follows:
when x is greater than y, x △ y = x ** y + x + y;
otherwise, x △ y = x + y + y + y.
The precedence of operations: □ > ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression... | {
"game_data": {
"answer": "21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 9 □ 4 □ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 △，规则如下：
当x是3的倍数时，x △ y = y - y * x；
其他情况下，x △ y = y + y / y * y - x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 △ 4 △ 3 / 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 4 △ 3 / 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x * y + y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1
Please fill your final answer... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ☆，规则如下：
当x是5的倍数时，x ☆ y = (y) + x；
其他情况下，x ☆ y = (y - x * y - x)。
和 △，规则如下：
当x和y的和是奇数时，x △ y = x - x ** x + x ☆ y；
其他情况下，x △ y = y - y ☆ x - y + x。
运算优先级：** = ☆ > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ☆ 2 △ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 2 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define △, the rules are as follows:
when y is odd, x △ y = (y) / 5 - 5 + y + x;
otherwise, x △ y = 4 / y + x - 3 - y.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expr... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x / y - x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 △ 3
Please fill your final an... | {
"game_data": {
"answer": "-2.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y * y * y * x * x.
and ○, the rules are as follows:
on the real number field, x ○ y = x * x * x / y ** y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y - 2 ♢ x + x.
The precedence of operations: ♢ = ○ = ♡ > ** > * = / = %... | {
"game_data": {
"answer": "343.000607",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 9 ♡ 1 ♢ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ○, the rules are as follows:
when y is a multiple of 5, x ○ y = x ** x + x + x + y;
otherwise, x ○ y = x - x + x * y.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of t... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 8 ○ 9 / 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = 5 + y + 3 - x * 4.
and △, the rules are as follows:
on the real number field, x △ y = y - y - x ◎ x * y.
The precedence of operations: ◎ > ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parenthese... | {
"game_data": {
"answer": "920",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 9 ◎ 9 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x / y * x - y * x.
and ◇, the rules are as follows:
when x is equal to y, x ◇ y = x - y * x □ x;
otherwise, x ◇ y = x * y - 3 * y.
The precedence of operations: ** = ◇ > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expr... | {
"game_data": {
"answer": "-9.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth... |
logic-v2 | Define ▽, the rules are as follows:
when y is odd, x ▽ y = x + x * y;
otherwise, x ▽ y = x * y * y ** x.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ▽ 9... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 9 % 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ◎, the rules are as follows:
when x and y are both even, x ◎ y = y - 4 - x - x;
otherwise, x ◎ y = y - x + y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y + y * x + x.
The precedence of operations: ** = ☆ > * = / = % > + = - = ◎。
Parentheses have the highest priority, and the expres... | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = (y / x) + x - y - 5.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y * abs(x).
and ♢, the rules are as follows:
when x is a multiple of 5, x ♢ y = x / x + y - y + x;
otherwise, x ♢ y = y - x ◇ y.
The precedence of operati... | {
"game_data": {
"answer": "-160",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 5 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 △，规则如下：
当x是5的倍数时，x △ y = x - (2 + y * x - x)；
其他情况下，x △ y = abs(y) / y - x。
运算优先级：** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 + 2 △ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 + 2 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ♡, the rules are as follows:
when x is less than y, x ♡ y = y + x - x + x;
otherwise, x ♡ y = (x / y * y).
and ⊗, the rules are as follows:
when the sum of x and y is even, x ⊗ y = x ♡ 5 - y;
otherwise, x ⊗ y = y / x + y - x.
The precedence of operations: ** > * = / = % > + = - = ♡ = ⊗。
Parentheses have ... | {
"game_data": {
"answer": "-4.555556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 1 ⊗ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 △，规则如下：
当x大于y时，x △ y = x - y * abs(x)；
其他情况下，x △ y = x / y。
运算优先级：** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y * x - x - x。
和 ◎，规则如下：
实数域上，x ◎ y = y ☆ x + x。
运算优先级：** = ☆ > * = / = % = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◎ 7 ☆ 4 ☆ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "260",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 7 ☆ 4 ☆ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = 1 - (x * y) - 4.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x / y - x.
and △, the rules are as follows:
when y is a multiple of 3, x △ y = x - x * y;
otherwise, x △ y = abs(2 * x * y) - x.
The precedence of operations:... | {
"game_data": {
"answer": "477",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 6 △ 6 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * y + x - x.
and ▽, the rules are as follows:
when x is greater than y, x ▽ y = x / x - y;
otherwise, x ▽ y = y / y - y - abs(x).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = 4 + x + y ▽ 5.
The precedence of operations... | {
"game_data": {
"answer": "-10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 2 ⊗ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y * y + y - x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = (x) * y - x - y.
The precedence of operations: ◎ > ** > * = / = % = ♡ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is c... | {
"game_data": {
"answer": "-1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 6 ♡ 9 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ◇, the rules are as follows:
when x is a multiple of 5, x ◇ y = 2 + y - x / 4;
otherwise, x ◇ y = x + 3 * 1 * y / y.
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of th... | {
"game_data": {
"answer": "48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 4 % 8 * 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ♢，规则如下：
当x和y都是奇数时，x ♢ y = 5 / y - x；
其他情况下，x ♢ y = y / 2 - x。
和 △，规则如下：
当y是偶数时，x △ y = x + y + x；
其他情况下，x △ y = (x * y)。
和 ◇，规则如下：
实数域上，x ◇ y = y * y + x。
运算优先级：♢ > ** > * = / = % = ◇ > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ♢ 1 △ 6 ◇ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♢ 1 △ 6 ◇ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x / y.
and ○, the rules are as follows:
when y is a multiple of 3, x ○ y = x + y * x;
otherwise, x ○ y = y - x + x.
The precedence of operations: ☆ > ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside t... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = abs(x / x - x - y) + x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x * (y + y / 1)。
和 ☆，规则如下：
当x和y的和是偶数时，x ☆ y = y ** y + x * x + x；
其他情况下，x ☆ y = (x) * y。
和 ◎，规则如下：
当x和y的和是奇数时，x ◎ y = y - (y) * x + y ☆ y；
其他情况下，x ◎ y = y ◇ y ** x + x + x。
运算优先级：◎ > ** = ◇ > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ☆ 7 ◇ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1260",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 7 ◇ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ▽，规则如下：
当x是3的倍数时，x ▽ y = x + x - y * x；
其他情况下，x ▽ y = x - y - 2 / x。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x * y + y / x。
和 △，规则如下：
实数域上，x △ y = (y ** x) - x □ y。
运算优先级：□ = △ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 □ 1 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "157.819336",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 1 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 □，规则如下：
当x小于y时，x □ y = x * y - y；
其他情况下，x □ y = x + y。
和 ○，规则如下：
实数域上，x ○ y = x □ y * 3。
运算优先级：** > * = / = % = □ > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 + 2 □ 10 * 2 ○ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "90",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 + 2 □ 10 * 2 ○ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ○，规则如下：
当y是5的倍数时，x ○ y = x + x / y - x；
其他情况下，x ○ y = abs(x + 2) / y * 1。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = x + x - y;
otherwise, x ⊙ y = y - y - x - x * x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = abs(x - 2 + y).
and ○, the rules are as follows:
on the real number field, x ○ y = (x + y) ♡ y.
The precedence of operat... | {
"game_data": {
"answer": "-506",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 5 + 7 ○ 2 ⊙ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ⊙，规则如下：
当x是偶数时，x ⊙ y = y - y * x；
其他情况下，x ⊙ y = y * x ** x。
和 ☆，规则如下：
实数域上，x ☆ y = y ⊙ y * x。
和 ○，规则如下：
当x是奇数时，x ○ y = y ☆ y * x；
其他情况下，x ○ y = x + y * y。
运算优先级：○ > ⊙ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ○ 8 ☆ 4 + 5 ⊙ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "31753",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 8 ☆ 4 + 5 ⊙ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = (4 + y + x)。
和 ○，规则如下：
当x小于y时，x ○ y = x / y；
其他情况下，x ○ y = y - x - abs(x + 5)。
运算优先级：♡ > ** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ♡ 4 ○ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 4 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ◎, the rules are as follows:
when x is even, x ◎ y = x * y - y ** 5;
otherwise, x ◎ y = y * 1 / y / x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * y + x ◎ y.
The precedence of operations: ◎ > ** = ⊗ > * = / = % > + = -。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "-24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = (x * y * 4).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = (x ⊙ x) + y.
and ♡, the rules are as follows:
when y is a multiple of 5, x ♡ y = y + x - y;
otherwise, x ♡ y = x + (x + y).
The precedence of operations: ♡ > ⊙ = ... | {
"game_data": {
"answer": "331",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 2 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ♡, the rules are as follows:
when x is odd, x ♡ y = 5 * x * y;
otherwise, x ♡ y = 2 * y + x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x + y - y.
The precedence of operations: ** = ▽ > * = / = % = ♡ > + = -。
Parentheses have the highest priority, and the expression inside the paren... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ♢，规则如下：
当y是3的倍数时，x ♢ y = y + x - x；
其他情况下，x ♢ y = y + x * x。
和 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = x ♢ y；
其他情况下，x ⊗ y = y * x ♢ y。
和 ⊙，规则如下：
当y是3的倍数时，x ⊙ y = y ♢ x；
其他情况下，x ⊙ y = x / x / y。
运算优先级：** = ♢ > * = / = % = ⊗ > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ♢ 6 ⊙ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 6 ⊙ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x * y / x。
和 ▽，规则如下：
实数域上，x ▽ y = x + 4 * x - y。
和 ♢，规则如下：
实数域上，x ♢ y = x / y ⊕ x。
运算优先级：▽ = ♢ > ** > * = / = % > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♢ 3 ⊕ 9 ▽ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "42",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 3 ⊕ 9 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ▽，规则如下：
当x等于y时，x ▽ y = 5 + y - abs(x) * 5；
其他情况下，x ▽ y = x * y * x * 2。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y - y - x。
和 ☆，规则如下：
当x小于y时，x ☆ y = y + x；
其他情况下，x ☆ y = abs(y * x - y)。
和 □，规则如下：
实数域上，x □ y = y * x + x。
运算优先级：☆ > ⊗ > ** > * = / = % > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 □ 9 ⊗ 10 ☆ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-64",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 9 ⊗ 10 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = y * y / x - y + 5.
and ♢, the rules are as follows:
when y is a multiple of 3, x ♢ y = 4 ▽ y * y - y + x;
otherwise, x ♢ y = y / y * y / y + x.
The precedence of operations: ** > * = / = % = ♢ > + = - = ▽。
Parentheses have the highest priority,... | {
"game_data": {
"answer": "4.73913",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 4 ▽ 1 ♢ 1 ♢ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = (y / x) * y。
和 △，规则如下：
实数域上，x △ y = y / x - x。
和 □，规则如下：
实数域上，x □ y = y + x + y。
运算优先级：⊗ > ** = □ > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 △ 9 ⊗ 10 □ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4.861111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 9 ⊗ 10 □ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ☆，规则如下：
当y是5的倍数时，x ☆ y = y * x + 2；
其他情况下，x ☆ y = y + (x) / y。
和 ♢，规则如下：
当x是偶数时，x ♢ y = y * x；
其他情况下，x ♢ y = x / y - x。
运算优先级：☆ > ** > * = / = % > + = - = ♢。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ☆ 1 ♢ 1 ♢ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 1 ♢ 1 ♢ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y * x - 1 * x + 2。
和 ◇，规则如下：
实数域上，x ◇ y = y ** y + y + x - y。
和 ○，规则如下：
当y是偶数时，x ○ y = y ⊕ x + 4 + x；
其他情况下，x ○ y = x * y - y / y。
运算优先级：◇ > ** = ⊕ > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ○ 4 ◇ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 4 ◇ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x ** x - y。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = 2 + y * x.
and ○, the rules are as follows:
when x is greater than y, x ○ y = x / y ⊗ y;
otherwise, x ○ y = x ⊗ y - x.
and ⊙, the rules are as follows:
when x is greater than y, x ⊙ y = 3 - x * y;
otherwise, x ⊙ y = x * x - y.
The precedenc... | {
"game_data": {
"answer": "-1239",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 4 ⊗ 10 ⊙ 6 ** 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x - y * x / 3。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y - x + 4 / y。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 □，规则如下：
当x是5的倍数时，x □ y = 1 * x * y；
其他情况下，x □ y = y * x - y。
和 ◇，规则如下：
实数域上，x ◇ y = y / 3 - x □ y。
运算优先级：** > * = / = % > + = - = □ = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 7 / 10 □ 8 ◇ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "33.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 7 / 10 □ 8 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ⊕, the rules are as follows:
when y is odd, x ⊕ y = (x / y - x);
otherwise, x ⊕ y = (y - x) - y.
and □, the rules are as follows:
when y is a multiple of 3, x □ y = y + x ⊕ x ** x;
otherwise, x □ y = y ⊕ x * y + x.
and ◎, the rules are as follows:
when y is a multiple of 5, x ◎ y = x □ y + y + y;
other... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 1 ⊕ 2 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x - y * y。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ○ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-93",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth... |
logic-v2 | 定义 ○，规则如下：
当x和y都是奇数时，x ○ y = x * y + x + y；
其他情况下，x ○ y = (y + y - y + x)。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ** 1 % 2 ○ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ** 1 % 2 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = (5 + y + x + 3);
otherwise, x ♡ y = abs(y + x).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x - x / y + x.
The precedence of operations: ⊗ > ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the... | {
"game_data": {
"answer": "7.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 2 ⊗ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y - (x * x)。
和 ♡，规则如下：
实数域上，x ♡ y = x - x - y。
运算优先级：** = □ > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 3 ♡ 2 ** 4 * 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-112",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 3 ♡ 2 ** 4 * 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define ◎, the rules are as follows:
when y is odd, x ◎ y = 1 / y * x ** x;
otherwise, x ◎ y = x - y * y - x - y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x - y / x / x.
and △, the rules are as follows:
when y is a multiple of 5, x △ y = y ◇ 2 * x * 4;
otherwise, x △ y = x * x ** y + ... | {
"game_data": {
"answer": "-47393.04",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 6 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ○, the rules are as follows:
when x is even, x ○ y = x * x + y + x + y;
otherwise, x ○ y = y - 3 - y - x.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expressio... | {
"game_data": {
"answer": "-7.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 / 2 ○ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ◇，规则如下：
当x是5的倍数时，x ◇ y = y / x；
其他情况下，x ◇ y = abs(y * x + y)。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = y - x + x.
and ⊙, the rules are as follows:
when x is less than y, x ⊙ y = 1 + abs(y) + x;
otherwise, x ⊙ y = y + x - x.
and □, the rules are as follows:
on the real number field, x □ y = x + x ⊙ y.
The precedence of operations: ⊙ > ** = □ > ... | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 10 □ 10 ⊙ 2 □ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = y * 2 - x;
otherwise, x ▽ y = x - x + y * y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expres... | {
"game_data": {
"answer": "93",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 - 10 + 7 ▽ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y * y / x ** 2.
and ◎, the rules are as follows:
when x is odd, x ◎ y = x + 3 + y + x;
otherwise, x ◎ y = x + y.
The precedence of operations: ** = ♡ = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the ... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 3 ◎ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define □, the rules are as follows:
when x and y are both odd, x □ y = x * y * y + y;
otherwise, x □ y = x * y.
and ○, the rules are as follows:
when the sum of x and y is odd, x ○ y = x + (y);
otherwise, x ○ y = y □ x - y.
The precedence of operations: □ = ○ > ** > * = / = % > + = -。
Parentheses have the highe... | {
"game_data": {
"answer": "126",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 6 □ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ○，规则如下：
当x和y都是奇数时，x ○ y = (x) / y；
其他情况下，x ○ y = x + (x + y)。
运算优先级：** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y + x * 4.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * x + y.
The precedence of operations: ☆ > ⊕ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "430",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 10 ⊕ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ⊕, the rules are as follows:
when y is odd, x ⊕ y = y - 5 ** x / y;
otherwise, x ⊕ y = x + x / y.
and □, the rules are as follows:
when the sum of x and y is even, x □ y = x / x + x + y;
otherwise, x □ y = x ⊕ y * x + y.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x / y + y + 5.
... | {
"game_data": {
"answer": "6.47619",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊕ 3 ♢ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ⊗, the rules are as follows:
when the sum of x and y is odd, x ⊗ y = abs(y + x / x + y) - x;
otherwise, x ⊗ y = 5 + y - (x) - y.
and ○, the rules are as follows:
when x is equal to y, x ○ y = x + y * y - 3;
otherwise, x ○ y = x - x ** y ⊗ y * x.
and ⊕, the rules are as follows:
on the real number field, ... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 4 * 7 ⊗ 5 ○ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y + x * x。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x + x + y - y * y。
和 ◎，规则如下：
实数域上，x ◎ y = x □ y + 1 * y。
运算优先级：□ > ** = ◎ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ◎ 3 ◎ 1 □ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-330",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 3 ◎ 1 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ▽，规则如下：
当x等于y时，x ▽ y = y - abs(x / x)；
其他情况下，x ▽ y = y / abs(x ** y)。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ▽ 7 ▽ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.055556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 7 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = y * x * y ** 3.
and ▽, the rules are as follows:
on the real number field, x ▽ y = 5 - x - y + 1.
and △, the rules are as follows:
on the real number field, x △ y = y + (x * x) + x.
The precedence of operations: ▽ = △ > ** = ⊗ > * = / = % > + =... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 8 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ⊕, the rules are as follows:
when x is greater than y, x ⊕ y = x - y + y;
otherwise, x ⊕ y = 3 + y / x.
and ⊗, the rules are as follows:
when x is less than y, x ⊗ y = (x) + y ⊕ x;
otherwise, x ⊗ y = (y ⊕ 3) - x.
and ♡, the rules are as follows:
when x is greater than y, x ♡ y = x + (y + x);
otherwise,... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 3 ⊕ 8 ⊗ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = (x / y - x - x + x)。
和 ◇，规则如下：
实数域上，x ◇ y = x * x / (3 * y) * y。
运算优先级：♡ > ** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◇ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x + y - x * y。
和 ◇，规则如下：
实数域上，x ◇ y = 2 - x + x - y ⊗ y。
和 ○，规则如下：
实数域上，x ○ y = x + y - 1 ⊗ 4 * 3。
运算优先级：** = ⊗ > * = / = % = ◇ > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ◇ 8 ⊗ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1765",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 8 ⊗ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = y * x。
和 □，规则如下：
当x是3的倍数时，x □ y = y / x；
其他情况下，x □ y = x * x * y。
运算优先级：□ > ** > * = / = % = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ♡ 1 □ 4 % 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 1 □ 4 % 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = 1 - y * x - 4。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define △, the rules are as follows:
when x is even, x △ y = y - x * x;
otherwise, x △ y = (x) - y - x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 * 10 ... | {
"game_data": {
"answer": "-190",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 * 10 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ☆，规则如下：
当x小于y时，x ☆ y = x / y * x；
其他情况下，x ☆ y = (y) * x + y。
和 ⊕，规则如下：
当x等于y时，x ⊕ y = abs(x + y + y)；
其他情况下，x ⊕ y = y * x。
运算优先级：☆ = ⊕ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ⊕ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊕ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = 3 * y - x.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1
Please fill your final answer... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y / x。
运算优先级：** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 * 3 △ 8 * 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 * 3 △ 8 * 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ▽，规则如下：
当x小于y时，x ▽ y = x - x * y * x；
其他情况下，x ▽ y = x * x - y - y。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊙, the rules are as follows:
when x and y are both odd, x ⊙ y = 2 - (y) - x;
otherwise, x ⊙ y = y * x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y + x ⊙ 1.
and △, the rules are as follows:
on the real number field, x △ y = y * x * y.
The precedence of operations: △ > ** = ⊙ > * =... | {
"game_data": {
"answer": "580",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 9 △ 8 ⊕ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = y - y * y + x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * x * y.
and ▽, the rules are as follows:
when x is less than y, x ▽ y = y ⊙ x - y;
otherwise, x ▽ y = y ⊗ x - y.
The precedence of operations: ⊙ > ** = ⊗ > *... | {
"game_data": {
"answer": "-20592",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 6 ▽ 6 ⊗ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 ☆，规则如下：
当x大于y时，x ☆ y = x - y / x；
其他情况下，x ☆ y = x - y + x。
和 ⊗，规则如下：
实数域上，x ⊗ y = y + x ☆ x。
运算优先级：☆ > ** > * = / = % = ⊗ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ☆ 1 ⊗ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "18.9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 1 ⊗ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y * y * y - x * x。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 △，规则如下：
当x是3的倍数时，x △ y = y + (y + 3 + x - x)；
其他情况下，x △ y = abs(x + x) * x * y - y。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ◇, the rules are as follows:
when x is a multiple of 5, x ◇ y = 5 - abs(y) * x - y - y;
otherwise, x ◇ y = x + y * 5 - 2 * y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the va... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = x - y - x。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ▽ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth... |
logic-v2 | Define □, the rules are as follows:
when x and y are both even, x □ y = abs(x + x) + 2 * y;
otherwise, x □ y = (y - 2 * x).
and ♡, the rules are as follows:
on the real number field, x ♡ y = x □ y + y ** y.
The precedence of operations: ** = ♡ > * = / = % = □ > + = -。
Parentheses have the highest priority, and th... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 3 ♡ 3 □ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ○, the rules are as follows:
when the sum of x and y is even, x ○ y = y / 4 ** x;
otherwise, x ○ y = x - abs(y - y).
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of th... | {
"game_data": {
"answer": "0.006836",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 7 % 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ○, the rules are as follows:
when y is odd, x ○ y = x - abs(y * 2);
otherwise, x ○ y = abs(y) * x.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1
Pl... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
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