env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ▽, the rules are as follows:
when x is even, x ▽ y = x - x - y * y / x;
otherwise, x ▽ y = 5 * y + 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 expre... | {
"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 = y - 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 expression: 6 - 2 ◇ 7
Please fill your fi... | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 2 ◇ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊙，规则如下：
当y是奇数时，x ⊙ y = x * y + 1 * 4；
其他情况下，x ⊙ y = x + y - y。
和 ▽，规则如下：
当x是奇数时，x ▽ y = (y ⊙ x + 2 + y)；
其他情况下，x ▽ y = x * (x + y ⊙ x + 4)。
和 ♡，规则如下：
当y是偶数时，x ♡ y = y - x - y；
其他情况下，x ♡ 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: 1 ▽ 8 ♡ 7
请将最终答案填入\boxed... | {
"game_data": {
"answer": "6",
"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_dept... |
logic-v2 | 定义 ⊗，规则如下：
当x是3的倍数时，x ⊗ y = x - (y) * y + y；
其他情况下，x ⊗ y = x / (y) + y。
和 ◇，规则如下：
实数域上，x ◇ y = x ⊗ (y) - x。
和 ☆，规则如下：
当x小于y时，x ☆ y = x - 5 * y - y；
其他情况下，x ☆ 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: 2 ☆ 7 ◇ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 7 ◇ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = 1 + y + y / x ** x.
and ○, the rules are as follows:
on the real number field, x ○ y = x + x + y - x + x.
and ◎, the rules are as follows:
when x is even, x ◎ y = (y / x * y) * y - y;
otherwise, x ◎ y = 3 * y + y + y ○ x.
The precedence of op... | {
"game_data": {
"answer": "232.000001",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 9 ◎ 10 ○ 10 ◎ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + y - 3 / x.
and ○, the rules are as follows:
on the real number field, x ○ y = x * y * y ⊙ y.
and △, the rules are as follows:
on the real number field, x △ y = x + 3 - y * x.
The precedence of operations: ○ > ** = △ > * = / = % = ⊙ > + = -。... | {
"game_data": {
"answer": "-3281.925",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 10 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define □, the rules are as follows:
when y is a multiple of 3, x □ y = y * y + x;
otherwise, x □ y = x * y * abs(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 expre... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"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y是奇数时，x ▽ y = y ** x + y；
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: 4 ▽ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "630",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 5",
"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 = y * x - y + 5.
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: 10 ▽ 10
Please fill your fi... | {
"game_data": {
"answer": "95",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 10",
"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5的倍数时，x ▽ y = x / abs(y * 1) - x；
其他情况下，x ▽ y = y + x + 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: 3 ▽ 8 ▽ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-17.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 8 ▽ 2",
"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 = y - y / x + y;
otherwise, x ▽ y = x - x / 3 / x * y.
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value ... | {
"game_data": {
"answer": "37.142857",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 8 % 3 * 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = x + (x * y - y) + y.
and ◇, the rules are as follows:
when the sum of x and y is even, x ◇ y = 2 * x * 4 + y - y;
otherwise, x ◇ y = x / y * x ♡ 1 / y.
The precedence of operations: ** = ◇ > * = / = % = ♡ > + = -。
Parentheses have the highest p... | {
"game_data": {
"answer": "0.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 2",
"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 = y * x + (x * y)。
和 ♡，规则如下：
当x是偶数时，x ♡ y = x + y - y ☆ x；
其他情况下，x ♡ 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: 5 ♡ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "225",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 3",
"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 = x + x * y + x.
and □, the rules are as follows:
on the real number field, x □ y = 4 * y * x / y ♢ 5.
and △, the rules are as follows:
when x is greater than y, x △ y = (x * y / x + 3);
otherwise, x △ y = x □ x * y + 1 + x.
The precedence of o... | {
"game_data": {
"answer": "52.979592",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 5 □ 5 ♢ 8",
"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 even, x ♡ y = y + x + x;
otherwise, x ♡ y = 4 * y - x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y * x + x.
The precedence of operations: ** > * = / = % > + = - = ♡ = ◎。
Parentheses have the highest priority, and the expression inside the pare... | {
"game_data": {
"answer": "70",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 9",
"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大于y时，x △ y = x * y / x；
其他情况下，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: 6 - 6 ** 7 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 6 ** 7 △ 5",
"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 = y - x - y.
and △, the rules are as follows:
on the real number field, x △ y = (x + x) + x + x - y.
The precedence of operations: ☆ = △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is c... | {
"game_data": {
"answer": "-3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 5",
"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和y的和是偶数时，x ♡ y = x * y / y + 5；
其他情况下，x ♡ y = y + x / x * 3。
和 ◇，规则如下：
当x是偶数时，x ◇ y = x + 4 * y / y；
其他情况下，x ◇ y = 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: 3 ◇ 2 % 5 ♡ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 2 % 5 ♡ 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 = 3 * 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: 10 ▽ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "31",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 4",
"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 = 4 + x / y - y - 5。
和 ♢，规则如下：
当x是5的倍数时，x ♢ y = y + x - x；
其他情况下，x ♢ y = 4 - 4 ** 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 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-7.428571",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 7",
"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 and y are both odd, x ♢ y = y * x / x;
otherwise, x ♢ y = x * y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y + x * x.
and □, the rules are as follows:
when x is a multiple of 3, x □ y = x ☆ 4 * y;
otherwise, x □ y = x / (y + y).
The precedenc... | {
"game_data": {
"answer": "1021.62963",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 3 ☆ 10 ☆ 7 ♢ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ▽，规则如下：
当y是5的倍数时，x ▽ y = y - x - y；
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: 9 + 5 ▽ 1 + 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 + 5 ▽ 1 + 3",
"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 = x / y / y * 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: 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 / y + x。
和 ⊕，规则如下：
当x和y都是奇数时，x ⊕ y = y - x - x；
其他情况下，x ⊕ y = x + x + y。
和 ♡，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: 9 ⊗ 4 ♡ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 4 ♡ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 △，规则如下：
当x大于y时，x △ y = y + x + 1；
其他情况下，x △ 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: 6 + 9 △ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "23",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 + 9 △ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x + y.
and ♡, the rules are as follows:
when x is a multiple of 5, x ♡ y = x - (x ** y);
otherwise, x ♡ y = x ◎ y.
The precedence of operations: ◎ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression inside th... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 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 * x - y.
and ⊗, the rules are as follows:
when y is a multiple of 3, x ⊗ y = x * 1 * y + 1;
otherwise, x ⊗ y = x - x ** y + x.
The precedence of operations: ⊗ > ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expres... | {
"game_data": {
"answer": "34964",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊗ 3 ⊗ 6 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 ⊕，规则如下：
当y是偶数时，x ⊕ y = 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 * y * x - y * y。
和 ◇，规则如下：
实数域上，x ◇ 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 - 2 ◇ 8 ♢ 8 ⊕ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-442",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 - 2 ◇ 8 ♢ 8 ⊕ 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 = x - abs(3 / x - y).
and ○, the rules are as follows:
on the real number field, x ○ y = x - y / x + y.
and △, the rules are as follows:
on the real number field, x △ y = y + y - (y ** x).
The precedence of operations: ⊙ = △ > ** > * = / = % = ○ ... | {
"game_data": {
"answer": "15.875",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊙ 5 △ 8",
"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 + 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 expression: 8 ♡ 3 + 2
Please fill your ... | {
"game_data": {
"answer": "32",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♡ 3 + 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ♢，规则如下：
当x是偶数时，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 = x + y。
和 ⊙，规则如下：
当x等于y时，x ⊙ y = y * y - x * x；
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: 2 ⊙ 3 ♢ 1 ○ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 3 ♢ 1 ○ 3",
"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 a multiple of 5, x ⊕ y = x / abs(x + x - x) * y;
otherwise, x ⊕ y = x - x / y - y * 1.
and ◇, the rules are as follows:
when y is a multiple of 3, x ◇ y = y - 3 - 3 ⊕ x + x;
otherwise, x ◇ y = y + 1 * x + y - x.
and □, the rules are as follows:
when x is odd, x □ y ... | {
"game_data": {
"answer": "28.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 10 ◇ 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：
实数域上，x ○ 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 ○ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 % 7 ○ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = (1 + 2 - x - y - 4).
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: 8 / 10 ◇ 4
Please fil... | {
"game_data": {
"answer": "-0.533333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 / 10 ◇ 4",
"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等于y时，x ◎ y = x + y；
其他情况下，x ◎ y = y + y - 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: 4 △ 9 ◎ 6 △ 10 △ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 9 ◎ 6 △ 10 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define ⊗, the rules are as follows:
when x is equal to y, x ⊗ y = x + x + abs(y) + x;
otherwise, x ⊗ y = x * 3 + x * (y / x).
and ♡, the rules are as follows:
when y is a multiple of 3, x ♡ y = x - x + x ⊗ y - y;
otherwise, x ♡ y = y / x + y + y + 3.
and □, the rules are as follows:
on the real number field, x ... | {
"game_data": {
"answer": "674.1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 7 ⊗ 4 □ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ○, the rules are as follows:
when x is odd, x ○ y = x + y - x + y;
otherwise, x ○ y = abs(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: 8... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 / 8 ○ 5",
"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 is less than y, x ◇ y = abs(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 expressio... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"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3的倍数时，x ◎ y = y - x - x；
其他情况下，x ◎ y = x + y * x。
和 ◇，规则如下：
当y是奇数时，x ◇ y = y + y * x；
其他情况下，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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 1",
"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 = y / x ** x - x - 5.
and ○, the rules are as follows:
on the real number field, x ○ y = y ⊕ 4 / y * y + x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x - x * y ○ y.
The precedence of operations: ** = ▽ > * = / = % > + = -... | {
"game_data": {
"answer": "-19.651068",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ○ 4 ⊕ 3 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y + 1 + 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
Please fill your final answer... | {
"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 | 定义 △，规则如下：
实数域上，x △ y = x + 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 △ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 2",
"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 = y - x - y - x / x；
其他情况下，x ☆ y = x - y - y - x。
和 ◇，规则如下：
当y是偶数时，x ◇ y = x + x - y / x - x；
其他情况下，x ◇ y = 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: 6 - 4 ◇ 2 ☆ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 4 ◇ 2 ☆ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define □, the rules are as follows:
when x is a multiple of 3, x □ y = y * x + x;
otherwise, x □ y = (y) - y ** x.
and △, the rules are as follows:
on the real number field, x △ y = x - y * 3.
The precedence of operations: □ = △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression i... | {
"game_data": {
"answer": "-17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 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 = 3 + (3 + y) * y * x。
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: 10 ◇ 2 + 6 ◎ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "93",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 2 + 6 ◎ 2",
"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 = 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: 3 - 8 ◇ 4 + 8
Please fill your fina... | {
"game_data": {
"answer": "-1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 - 8 ◇ 4 + 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 = abs(2 + 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: 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"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 = abs(x + y) * y。
和 ♡，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: 8 □ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 2",
"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 y is a multiple of 5, x ⊕ y = y - y * x;
otherwise, x ⊕ y = x * x * y.
and ♢, 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 = abs(y - y + x);
otherwise, x ⊙ y = y ⊕ y - x.
The prece... | {
"game_data": {
"answer": "-0.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊕ 2 ⊙ 1 ♢ 3",
"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 * x + x + x * y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y + y * 2 ☆ y - x.
The precedence of operations: ☆ = ⊗ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parenthese... | {
"game_data": {
"answer": "703",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 3 ☆ 9",
"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 equal to y, x ⊗ y = x ** y * y + y;
otherwise, x ⊗ y = x * y - (y - y) - y.
and ○, the rules are as follows:
on the real number field, x ○ y = y + x * y + x + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = 4 + y ⊗ y - x * 1.
The precedence of ... | {
"game_data": {
"answer": "-1486",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 * 3 ⊗ 5 ○ 10 ◎ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define □, the rules are as follows:
when x is equal to y, x □ y = x + y - x ** 2;
otherwise, x □ y = y + (x ** x + y).
and ♢, the rules are as follows:
on the real number field, x ♢ y = x - 1 * y / x.
The precedence of operations: ** = ♢ > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expr... | {
"game_data": {
"answer": "157.777778",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 8 * 9 ♢ 10",
"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 + 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 ◇ 2 / 5 ◇ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 2 / 5 ◇ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x / y。
和 ◎，规则如下：
实数域上，x ◎ y = x * y * 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 + 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 ♡ 5 ⊗ 6 ◎ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.518519",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♡ 5 ⊗ 6 ◎ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
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: 2 ○ 10 % 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 10 % 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ◇，规则如下：
当y是奇数时，x ◇ y = 5 / x ** 5 - x / y；
其他情况下，x ◇ y = x + x / 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 % 4 * 5 ◇ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 % 4 * 5 ◇ 8",
"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 = 5 - 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: 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"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y是偶数时，x ▽ y = y + x - y；
其他情况下，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 ▽ 6 - 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 6 - 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = x * y / x。
和 ▽，规则如下：
当x是5的倍数时，x ▽ y = 3 * x ⊙ y；
其他情况下，x ▽ y = y - y - x。
和 ⊗，规则如下：
当y是偶数时，x ⊗ y = y + x ▽ y；
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: 7 ⊗ 3 % 3 ▽ 5 ⊙ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 3 % 3 ▽ 5 ⊙ 9",
"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 greater than y, x ▽ y = abs(x * x * x - x + y);
otherwise, x ▽ y = x + abs(y - y + x) + y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y ▽ 2 * 3 * x + y.
and ⊗, the rules are as follows:
when the sum of x and y is even, x ⊗ y = 2 + y ♡ x + 3;
... | {
"game_data": {
"answer": "-166",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 4 ⊗ 7",
"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y是奇数时，x ▽ y = 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: 1 ▽ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 4",
"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 = abs(x) - x * y；
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: 2 ◇ 9 - 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 9 - 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ♡，规则如下：
当x是3的倍数时，x ♡ y = 3 * 2 / x - y；
其他情况下，x ♡ y = x + y * y - y - y。
和 ○，规则如下：
实数域上，x ○ y = 5 ♡ 2 ** 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: 3 ♡ 10 ○ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "42",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 10 ○ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ⊙，规则如下：
当x小于y时，x ⊙ y = (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 + 5。
和 □，规则如下：
实数域上，x □ y = abs(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: 7 ○ 10 □ 2 ⊙ 3 ○ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 10 □ 2 ⊙ 3 ○ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ☆，规则如下：
当x等于y时，x ☆ y = y / x；
其他情况下，x ☆ y = x + y。
和 ○，规则如下：
当y是奇数时，x ○ y = abs(x) - y * 5；
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: 1 ○ 6 ☆ 7 ○ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-63",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 6 ☆ 7 ○ 6",
"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 = y - 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 expression: 1 ◇ 7 + 8 ◇ 2
Please fill your ... | {
"game_data": {
"answer": "-9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 7 + 8 ◇ 2",
"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 3, x ⊙ y = y + (x * y / x);
otherwise, x ⊙ y = y + 2 + x.
and □, the rules are as follows:
when y is even, x □ y = (y + y / x);
otherwise, x □ y = x / abs(y - x).
and ☆, the rules are as follows:
when x and y are both even, x ☆ y = y □ x * x * x;
oth... | {
"game_data": {
"answer": "28",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 3 ☆ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
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: 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 - x * y。
和 ◇，规则如下：
当x是3的倍数时，x ◇ y = (x * y ⊙ x)；
其他情况下，x ◇ y = x ⊙ x * y。
和 □，规则如下：
当y是3的倍数时，x □ y = y + x ◇ 2；
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: 4 ⊙ 10 ◇ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-11988",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 10 ◇ 9",
"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 = x + x + y + y.
and □, the rules are as follows:
on the real number field, x □ y = x * y ⊕ (3 - y).
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x □ 5 * 2 + y.
The precedence of operations: □ > ⊕ > ** > * = / = % = ⊙ > + = ... | {
"game_data": {
"answer": "512",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 3 ⊙ 8",
"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 = y / (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: 4 ⊙ 7 ** 1 ◎ 3 ♢ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.000183",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 7 ** 1 ◎ 3 ♢ 6",
"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 even, x ◎ y = y / 4 * x - x - y;
otherwise, x ◎ y = (y + x - x) * x + x.
and ♡, the rules are as follows:
when y is even, x ♡ y = x + y - 1 ◎ 1;
otherwise, x ♡ y = x + x + y ◎ y + 2.
The precedence of operations: ♡ > ** > * = / = % = ◎ > + = -。
Parentheses have the ... | {
"game_data": {
"answer": "36",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 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:
on the real number field, x ◎ y = (y - x * x) - x.
and ○, the rules are as follows:
when x is less than y, x ○ y = y * x ◎ x - y;
otherwise, x ○ y = x ◎ y / (x * x).
The precedence of operations: ○ > ** > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the exp... | {
"game_data": {
"answer": "-102.864",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ○ 2 % 5 ◎ 9 * 10",
"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 = 3 - y * 3 + 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: 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：
当x小于y时，x ○ y = x + y - y；
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: 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 | Define ♡, the rules are as follows:
when y is even, x ♡ y = x / y + 1 + x;
otherwise, x ♡ y = y - y + y + x.
and □, the rules are as follows:
when x and y are both odd, x □ y = y + y - 4 + x;
otherwise, x □ y = y ♡ x * x * y.
The precedence of operations: ** > * = / = % > + = - = ♡ = □。
Parentheses have the hig... | {
"game_data": {
"answer": "2.027778",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y / x + y + y * y.
and □, the rules are as follows:
on the real number field, x □ y = y - x ⊙ x - y - x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y + x.
The precedence of operations: ** = ⊙ > * = / = % = ☆ > + = - = □。... | {
"game_data": {
"answer": "-5595.04",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 - 10 ☆ 10 ⊙ 8 □ 3",
"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。
和 ☆，规则如下：
实数域上，x ☆ y = abs(y - y ** x)。
和 ◇，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: 4 ♢ 1 ◇ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1024",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 1 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define ◎, the rules are as follows:
when x and y are both even, x ◎ y = y + x ** (y * x);
otherwise, x ◎ y = (y + x) + y + y.
and ♡, the rules are as follows:
when x is odd, x ♡ y = x ◎ x * y - y;
otherwise, x ♡ y = x / y - x.
The precedence of operations: ** = ◎ > * = / = % > + = - = ♡。
Parentheses have the hi... | {
"game_data": {
"answer": "-1.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 7 / 8 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = (x + y / 1).
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 ◇ 3
Please fill your final ... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 3",
"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(1 + 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: 10 △ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 2",
"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 = 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: 9 + 8 ⊙ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 + 8 ⊙ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ☆，规则如下：
当y是奇数时，x ☆ y = x - x - y；
其他情况下，x ☆ y = y * x + x - x。
和 ◇，规则如下：
当y是3的倍数时，x ◇ y = (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: 10 ☆ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 3",
"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 y is a multiple of 5, x ♡ y = y * x + y - x;
otherwise, x ♡ y = y - 2 * x / x.
and ⊕, the rules are as follows:
when x is greater than y, x ⊕ y = y + x + y;
otherwise, x ⊕ y = x ♡ y * y.
The precedence of operations: ⊕ > ** > * = / = % > + = - = ♡。
Parentheses have the h... | {
"game_data": {
"answer": "37",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♡ 5",
"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5的倍数时，x ♢ y = abs(y * x)；
其他情况下，x ♢ y = y - x + y。
和 ▽，规则如下：
实数域上，x ▽ y = x * x - y。
和 ♡，规则如下：
实数域上，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 ▽ 1 ♡ 4 ♢ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "630",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 1 ♡ 4 ♢ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
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: 3 % 9 ○ 6 ○ 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 % 9 ○ 6 ○ 1",
"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 - 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 the expression: 5
Please fill your final a... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"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y是3的倍数时，x ▽ y = (x - y * y) - x；
其他情况下，x ▽ y = x - y + 3 + 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: 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 + 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: 9 + 10 ▽ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "36",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 + 10 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
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 = x ○ y + y。
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: 5 ○ 5 ♢ 9 + 10 ⊗ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-12.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 5 ♢ 9 + 10 ⊗ 1",
"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 = 5 * 4 * x + 5 - y;
otherwise, x ◎ y = 1 + y * x * 5 + 4.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = (2 - y) * y / x - y.
The precedence of operations: ** = ◎ > * = / = % = ⊗ > + = -。
Parentheses have the highest priorit... | {
"game_data": {
"answer": "-3.001626",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 5 * 9 ⊗ 3",
"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 + 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: 3 ◇ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 8",
"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小于y时，x ☆ y = x + (y) * y；
其他情况下，x ☆ y = y * y + (x) * y。
和 ◇，规则如下：
实数域上，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: 3 ☆ 4 * 7 ◇ 8 ** 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1064",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 4 * 7 ◇ 8 ** 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | 定义 ◎，规则如下：
当y是奇数时，x ◎ y = (y + x + x * x)；
其他情况下，x ◎ y = y / x * 4 + y。
和 △，规则如下：
实数域上，x △ 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: 7 △ 7 + 6 ◎ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "52.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 7 + 6 ◎ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define △, the rules are as follows:
when the sum of x and y is odd, x △ y = y - y + x + x / y;
otherwise, x △ y = x * 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 va... | {
"game_data": {
"answer": "181.019336",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ** 2 ** 1 △ 4",
"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 / 2 * (4) - x * y。
和 ◎，规则如下：
当x等于y时，x ◎ y = y - y - x；
其他情况下，x ◎ y = 4 + y / x / 5。
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: 3 △ 2 ◎ 5 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "91.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 2 ◎ 5 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + 2 + y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x + x - y - y + y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = 1 * x + y - 4.
The precedence of operations: ** = ☆ = ⊗ > * = / = % > + = - = ⊕。... | {
"game_data": {
"answer": "21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 7 ⊕ 3 ⊗ 7 ⊗ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ◇, the rules are as follows:
when x is less than y, x ◇ y = x + y * (x) / y;
otherwise, x ◇ y = (x * y) * 5.
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": "40",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 2",
"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 = x + y - y；
其他情况下，x □ y = y + x * x + x。
和 ♢，规则如下：
当x和y都是奇数时，x ♢ y = y + abs(y * 2 - 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: 10 ♢ 2 □ 5 □ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.909091",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♢ 2 □ 5 □ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define ⊗, the rules are as follows:
when the sum of x and y is even, x ⊗ y = x * 1 + 4 * y;
otherwise, x ⊗ y = y - x / y * x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = 5 * x * y + 3 - 2.
The precedence of operations: ⊕ > ** > * = / = % > + = - = ⊗。
Parentheses have the highest priority, a... | {
"game_data": {
"answer": "-15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
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