env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = y * 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 expression: 6 ○ 9 + 3 - 6
Please fill y... | {
"game_data": {
"answer": "105",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 9 + 3 - 6",
"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 * 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 ○ 1
Please fill your final an... | {
"game_data": {
"answer": "65",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 1",
"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 even, x ⊙ y = 5 / (y / x);
otherwise, x ⊙ y = x ** y - x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = abs(y - y * x) + 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": "47.640625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊕ 9 ⊙ 8",
"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 = y + abs(1 * 4 * x * 4).
and ◇, the rules are as follows:
on the real number field, x ◇ y = (x) - x - y.
and ☆, the rules are as follows:
when x is greater than y, x ☆ y = x * y / (x ◇ x) / x;
otherwise, x ☆ y = x * (x + x - y / y).
The preced... | {
"game_data": {
"answer": "-0.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 2 ◇ 9 ** 10 ☆ 4",
"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 = 3 * x * y;
otherwise, x ♢ y = x ** y + y.
and ⊙, the rules are as follows:
when x is equal to y, x ⊙ y = x + y;
otherwise, x ⊙ y = 5 * x + y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x * x / y.
The precedence of operat... | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 3 ⊙ 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 y is a multiple of 3, x □ y = y - y - x;
otherwise, x □ y = y * x + 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 insi... | {
"game_data": {
"answer": "0.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 8 ⊗ 9 ** 4 □ 3",
"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 greater than y, x ☆ y = (x) - y - x;
otherwise, x ☆ y = y + 1 / x.
and ⊕, the rules are as follows:
when x and y are both odd, x ⊕ y = (y + x);
otherwise, x ⊕ y = x - y ☆ y.
The precedence of operations: ** > * = / = % = ☆ > + = - = ⊕。
Parentheses have the highest p... | {
"game_data": {
"answer": "-11.871212",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 1 ⊕ 2 ⊕ 4 ☆ 8",
"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 less than y, x ◇ y = 2 * x - x + y + y;
otherwise, x ◇ y = y + y + 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": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": nu... |
logic-v2 | 定义 ⊕，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 = x ⊕ y * x；
其他情况下，x ○ y = x / y。
和 △，规则如下：
当x是5的倍数时，x △ y = x + 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 ○ 2 * 7 △ 2 ⊕ 2 * 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "175",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ○ 2 * 7 △ 2 ⊕ 2 * 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ▽, the rules are as follows:
when x is a multiple of 3, x ▽ y = abs(y + x - x / y) * x;
otherwise, x ▽ y = y - x - y + 3.
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": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 6 ▽ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ▽，规则如下：
实数域上，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: 2 ▽ 2 / 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 2 / 2",
"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 + 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 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "57",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 6",
"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 is a multiple of 5, x ⊕ y = y - y + y * x / y;
otherwise, x ⊕ y = y * x - y - x + y.
and △, the rules are as follows:
on the real number field, x △ y = (2 * 1) ⊕ y + x - 5.
and ▽, the rules are as follows:
on the real number field, x ▽ y = 4 - y * x - x - x.
The preced... | {
"game_data": {
"answer": "25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 2 ⊕ 2 ** 2 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = 4 / 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 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 = x / (x * 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
Please fill your fi... | {
"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 + 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 ▽ 4
Please fill your final an... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 4",
"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是奇数时，x □ y = 5 * y - x - y；
其他情况下，x □ y = x - x * y * y。
和 ♢，规则如下：
当x和y都是奇数时，x ♢ y = (y * y) □ x；
其他情况下，x ♢ y = 4 - (x + y □ y)。
和 ▽，规则如下：
当x是5的倍数时，x ▽ y = x * x - 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: 2 ▽ 4 ♢ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 4 ♢ 2",
"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 = y * x；
其他情况下，x ◎ y = y - x + x。
和 ☆，规则如下：
当y是5的倍数时，x ☆ y = 1 + y * abs(x)；
其他情况下，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 ☆ 1 ☆ 4 ◎ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 1 ☆ 4 ◎ 5",
"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 even, x ☆ y = x + x - y * x;
otherwise, x ☆ y = x * y - 3 * x.
and ◇, the rules are as follows:
when x is less than y, x ◇ y = x * 5 * 5 + y;
otherwise, x ◇ y = y ☆ x / 1 - y.
The precedence of operations: ** > * = / = % = ◇ > + = - = ☆。
Parentheses... | {
"game_data": {
"answer": "40",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◇ 8",
"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 + y - 2.
and ♢, the rules are as follows:
when x is greater than y, x ♢ y = (x / y) ☆ y + y;
otherwise, x ♢ y = y * 2 * 2 - x.
The precedence of operations: ** > * = / = % > + = - = ☆ = ♢。
Parentheses have the highest priority, and the ex... | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 + 7 ☆ 9 ♢ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ☆，规则如下：
当y是偶数时，x ☆ y = x + y + y；
其他情况下，x ☆ y = y - x - y - x。
和 ○，规则如下：
当y是5的倍数时，x ○ y = y * y - y + x * y；
其他情况下，x ○ y = x - 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: 8 ○ 7 ☆ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 7 ☆ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ◇, the rules are as follows:
when the sum of x and y is even, x ◇ y = y * x;
otherwise, x ◇ y = abs(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 exp... | {
"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 = 5 / y * (x * y) - x.
and ♢, 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 = y ** 2 - y + y * x.
The precedence of operations: ** = ◎ > * = / = % = ⊕ > + =... | {
"game_data": {
"answer": "72",
"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_dep... |
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: 8 ◇ 1 ◇ 2
Please fill your fina... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 1 ◇ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x + y / y - y + y.
and △, the rules are as follows:
on the real number field, x △ y = x * x * x / y + y.
The precedence of operations: ** = □ > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parenthese... | {
"game_data": {
"answer": "31.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 10",
"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 = (x * y / y);
otherwise, x ⊕ y = y * x.
and ◇, the rules are as follows:
when x is a multiple of 5, x ◇ y = x + (x) + y;
otherwise, x ◇ y = x / y * x.
and ⊗, the rules are as follows:
when the sum of x and y is odd, x ⊗ y = y * x;
otherwis... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊕ 8 ⊗ 8 % 9 ⊗ 5 ◇ 6",
"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 * 4 / 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: 7 ♢ 10
Please fill your fin... | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 10",
"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 = 1 - x ** y.
and ◎, the rules are as follows:
when x is even, x ◎ y = y - y * x;
otherwise, x ◎ y = x / y - x.
and △, the rules are as follows:
when x is less than y, x △ y = x ◎ y + x;
otherwise, x △ y = y * x * y.
The precedence of operati... | {
"game_data": {
"answer": "45",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 6 ◎ 3",
"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 + y - 3；
其他情况下，x △ y = 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: 1 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 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：
实数域上，x □ y = x - x + y + x - y。
和 ⊗，规则如下：
实数域上，x ⊗ y = y + y + (x) + 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 □ 3 + 5 ⊗ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "28",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 3 + 5 ⊗ 7",
"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 - 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 ◇ 10 / 6 + 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 10 / 6 + 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ◇, the rules are as follows:
when the sum of x and y is even, x ◇ y = (y - x + x) * y;
otherwise, x ◇ y = x / y * 2 * x.
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value o... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 % 10 ◇ 5 - 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ⊕, the rules are as follows:
when y is a multiple of 5, x ⊕ y = y + y ** x - 4;
otherwise, x ⊕ y = y * x + y + x.
and ⊗, the rules are as follows:
when x is even, x ⊗ y = x + y * x - y;
otherwise, x ⊗ y = (x / 3 * y).
and ♢, the rules are as follows:
on the real number field, x ♢ y = y + y + x ⊕ x.
The... | {
"game_data": {
"answer": "-9422.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 - 10 ** 2 ⊕ 3 ♢ 6 ⊗ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types":... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y + x。
和 ⊙，规则如下：
当y是3的倍数时，x ⊙ y = 3 * x - y * 4；
其他情况下，x ⊙ y = y * 1 ⊕ x + y。
和 ♡，规则如下：
当x小于y时，x ♡ y = x * x - y ⊕ x；
其他情况下，x ♡ y = y * 2 + 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 ♡ 7 ⊙ 7 ⊕ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 7 ⊙ 7 ⊕ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 □，规则如下：
当x是奇数时，x □ y = y * x；
其他情况下，x □ y = 2 * x - y。
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: 6 □ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 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:
on the real number field, x ⊙ y = 3 * x * y.
and ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = (x) + y;
otherwise, x ♡ y = x + abs(y - x).
and ☆, the rules are as follows:
on the real number field, x ☆ y = y - x - y.
The precedence of operations: ** = ☆... | {
"game_data": {
"answer": "-2457",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 7 ⊙ 9 * 7 ☆ 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 and y are both even, x ☆ y = x + x - x + y;
otherwise, x ☆ y = 2 / 1 * 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 e... | {
"game_data": {
"answer": "-12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 7 * 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 = 5 * y * x - y。
和 ○，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 ◎ 5 □ 5 ◎ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "146",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 1 ◎ 5 □ 5 ◎ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define △, the rules are as follows:
when the sum of x and y is odd, x △ y = 5 + y + x * y;
otherwise, x △ y = y - 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 t... | {
"game_data": {
"answer": "68",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 % 7 △ 9",
"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和y的和是奇数时，x ⊕ y = x - y - x；
其他情况下，x ⊕ y = x * y * x / x。
和 ◇，规则如下：
当x是偶数时，x ◇ y = x ⊕ x / y / y；
其他情况下，x ◇ y = y + x。
和 ⊗，规则如下：
实数域上，x ⊗ y = 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: 6 ◇ 2 ⊗ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-84",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 2 ⊗ 6",
"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 - 3 + x - 2。
和 ⊙，规则如下：
实数域上，x ⊙ y = x + 2 - x ♢ y。
和 ◇，规则如下：
实数域上，x ◇ y = 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: 6 ◇ 4 ♢ 9 ⊙ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 4 ♢ 9 ⊙ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊕，规则如下：
当y是3的倍数时，x ⊕ y = x * x * y；
其他情况下，x ⊕ y = x ** y + x - abs(y)。
和 ♢，规则如下：
实数域上，x ♢ y = y + x。
和 ○，规则如下：
实数域上，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: 3 + 8 ⊕ 5 ♢ 1 ○ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 + 8 ⊕ 5 ♢ 1 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define ◇, the rules are as follows:
when y is a multiple of 5, x ◇ y = y * x - abs(y ** 1) + 1;
otherwise, x ◇ y = 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 v... | {
"game_data": {
"answer": "443",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 + 3 ◇ 9 ◇ 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 * x * 2.
and ♡, the rules are as follows:
when y is a multiple of 5, x ♡ y = (x - y) ⊙ x;
otherwise, x ♡ y = x + y - 5.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (4) ♡ x * y.
The precedence of operations: ** = ☆ > *... | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 1 ☆ 1 - 7 ♡ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
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:
when x is equal to y, x ⊗ y = 1 * y * x ♡ x;
otherwise, x ⊗ y = y / y ** x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y + (y ♡ y ** x).
The precedence of operations: ♡ >... | {
"game_data": {
"answer": "0.001953",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 1 ♡ 5 ☆ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x + y * 4。
和 ◇，规则如下：
当x小于y时，x ◇ y = x * abs(x + y - y)；
其他情况下，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: 10 ◇ 10 ◎ 8 ◇ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10665",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 10 ◎ 8 ◇ 5",
"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大于y时，x ☆ y = y - x - x * 3 + 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: 1 - 6 ☆ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "23",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 - 6 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ♢, the rules are as follows:
when x and y are both even, x ♢ y = y / x + x;
otherwise, x ♢ y = y + x + y.
and □, the rules are as follows:
on the real number field, x □ y = y + (x) + y.
and ♡, the rules are as follows:
when y is a multiple of 3, x ♡ y = y + (x □ y);
otherwise, x ♡ y = y + 3 + x.
The pr... | {
"game_data": {
"answer": "45",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♡ 5 □ 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 - y。
和 ○，规则如下：
实数域上，x ○ y = y - x * y。
和 ♢，规则如下：
实数域上，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: 1 ♢ 2 ○ 6 ⊗ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 2 ○ 6 ⊗ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ⊗, the rules are as follows:
when x is less than y, x ⊗ y = 2 * x + x ** (y);
otherwise, x ⊗ y = x + y * 4.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x * 1 * y + y.
and ⊙, the rules are as follows:
when x is a multiple of 3, x ⊙ y = y ⊗ y * x;
otherwise, x ⊙ y = y - y ♡ x + y.
... | {
"game_data": {
"answer": "72",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 3 ♡ 4",
"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 even, x ♢ y = x * y * 5;
otherwise, x ♢ y = x - y + y.
and ○, the rules are as follows:
when x is equal to y, x ○ y = x - (5 ♢ y);
otherwise, x ○ y = (y - y) + x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x ♢ y + y.
The precedence of opera... | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♢ 9 ⊕ 10",
"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y是3的倍数时，x ☆ y = x / y * (y + 4)；
其他情况下，x ☆ y = x - y - y - x * x。
和 ⊙，规则如下：
实数域上，x ⊙ y = 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: 6 ☆ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-50",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ☆ 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 y is odd, x ☆ y = y * y - x * x;
otherwise, x ☆ y = x / x - x * y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = 1 * y + x.
The precedence of operations: ⊙ > ** > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expression inside t... | {
"game_data": {
"answer": "-323",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 + 2 ⊙ 9 ⊙ 4 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | 定义 ◎，规则如下：
当x等于y时，x ◎ y = x - 3 ** (y)；
其他情况下，x ◎ y = y ** 4 - x + y。
和 ⊕，规则如下：
实数域上，x ⊕ y = 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4101",
"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 | Define ○, the rules are as follows:
on the real number field, x ○ y = y * 1 + 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: 2 ○ 2
Please fill your fina... | {
"game_data": {
"answer": "6",
"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:
when x is a multiple of 3, x ♡ y = x * y - y;
otherwise, x ♡ y = y - x * 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 in... | {
"game_data": {
"answer": "-26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 4 ♡ 2",
"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 = abs(x ** 4 * 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: 8
Please fill your fi... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"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 * (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 ◇ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 7",
"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。
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: 1 △ 2 ♡ 9 + 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "38",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 2 ♡ 9 + 10",
"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 = y * x * y。
和 ◇，规则如下：
实数域上，x ◇ y = 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 □ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "200",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 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:
when y is even, x △ y = x - y * x - x;
otherwise, x △ y = 4 + y - 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": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 * 8 △ 3 △ 3",
"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 odd, x ♢ y = (y - x) - y;
otherwise, x ♢ y = (y - y + x).
and ☆, the rules are as follows:
when x is a multiple of 5, x ☆ y = x / (y) - x;
otherwise, x ☆ y = y - x - x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x / x - y.
... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 3 ☆ 8 ⊙ 6 ♢ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x - x - x / x - y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y * y ⊗ x - x * y.
and □, the rules are as follows:
on the real number field, x □ y = 4 ▽ 2 - x * 5 * y.
The precedence of operations: ** = ⊗ = ▽ > * = / = % ... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 4 ⊗ 3 + 8 ▽ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * x * 3 + y.
and ◇, the rules are as follows:
when y is odd, x ◇ y = abs(y) + y - x;
otherwise, x ◇ y = (y - 5) + x ⊕ x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - x + y * x.
The precedence of operations: ** > * ... | {
"game_data": {
"answer": "208",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 1 ◇ 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：
当y是3的倍数时，x □ y = x * x * y - x；
其他情况下，x □ y = y - x / y。
和 ☆，规则如下：
实数域上，x ☆ y = 1 □ 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 □ 7 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20.761252",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 7 ☆ 7",
"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 = 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: 7 ** 2 * 2 ○ 2
Please fill your... | {
"game_data": {
"answer": "-94",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ** 2 * 2 ○ 2",
"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 a multiple of 3, x □ y = x * y * y;
otherwise, x □ y = x / y / 5.
and ⊕, the rules are as follows:
when y is a multiple of 3, x ⊕ y = y / 5 □ x;
otherwise, x ⊕ y = y □ x / y.
The precedence of operations: ⊕ > ** > * = / = % = □ > + = -。
Parentheses have the highest ... | {
"game_data": {
"answer": "3.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 6 ⊕ 9 ⊕ 9 ⊕ 8",
"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 = abs(x + y).
and ⊕, 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 greater than y, x □ y = y / x + y;
otherwise, x □ y = x * y ☆ y + x.
The precedence of operations: ☆ > **... | {
"game_data": {
"answer": "7.291667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 3 □ 3 ☆ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define ♡, the rules are as follows:
when x is a multiple of 5, x ♡ y = 3 / y * x;
otherwise, x ♡ y = abs(y * x + y).
and □, the rules are as follows:
when x is a multiple of 3, x □ y = x ♡ y / y;
otherwise, x □ y = x * y * y.
The precedence of operations: ♡ = □ > ** > * = / = % > + = -。
Parentheses have the hig... | {
"game_data": {
"answer": "95",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 3 ♡ 5",
"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 = x ** 5 - y + y + 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: 1 ◇ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 7",
"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 = 5 * y - x；
其他情况下，x ○ y = 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: 5 - 1 ○ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "156",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 - 1 ○ 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:
on the real number field, x □ y = y ** x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y * x / 4.
The precedence of operations: □ > ** > * = / = % = ⊗ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated fir... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 6 % 8 ⊗ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ☆，规则如下：
当y是5的倍数时，x ☆ y = y - y - 3 ** x；
其他情况下，x ☆ y = x - x * y - x。
和 ♢，规则如下：
实数域上，x ♢ y = 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: 10 ♢ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "12.571429",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♢ 7",
"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大于y时，x ⊗ y = abs(x) - x - y；
其他情况下，x ⊗ y = x + x * 2 - y。
和 ◎，规则如下：
当x是偶数时，x ◎ y = (x + 3 * y) - y；
其他情况下，x ◎ y = y * (x * 3 * 1)。
和 ⊕，规则如下：
当x是偶数时，x ⊕ y = x * y；
其他情况下，x ⊕ y = 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: 2 ⊗ 10 ⊕ 10
请将最终答案填入\boxed{}中... | {
"game_data": {
"answer": "-94",
"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_... |
logic-v2 | 定义 ☆，规则如下：
当y是5的倍数时，x ☆ y = x / y；
其他情况下，x ☆ y = x + y + y。
和 ▽，规则如下：
当x和y都是奇数时，x ▽ y = x * x + y；
其他情况下，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 ☆ 1 ▽ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ☆ 1 ☆ 1 ▽ 4",
"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 + y / x;
otherwise, x ○ y = x * abs(y) - y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y * y * x.
The precedence of operations: ○ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the expression... | {
"game_data": {
"answer": "4374",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 4 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define ⊗, the rules are as follows:
when x and y are both even, x ⊗ y = y + x;
otherwise, x ⊗ y = x / 1 * y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x - x * y.
and △, the rules are as follows:
on the real number field, x △ y = (x - y) - x.
The precedence of operations: ⊗ > ** = ⊙ = △ ... | {
"game_data": {
"answer": "-7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 5 ⊗ 4 △ 7",
"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大于y时，x ⊕ y = y * x / (x)；
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: 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 | 定义 ☆，规则如下：
实数域上，x ☆ y = x - 2 * y - y。
和 △，规则如下：
当x和y都是奇数时，x △ y = x / 5 * y；
其他情况下，x △ y = y + x ☆ 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: 9 △ 1 ** 8 ☆ 10 * 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5e-06",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 1 ** 8 ☆ 10 * 2",
"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)。
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: 3 ♢ 8 ☆ 7 / 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.777778",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 8 ☆ 7 / 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define ⊙, the rules are as follows:
when x is less than y, x ⊙ y = x * x * y - 5;
otherwise, x ⊙ y = x / 3 / abs(y) * y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y - y * x.
The precedence of operations: ⊗ > ** = ⊙ > * = / = % > + = -。
Parentheses have the highest priority, and the expres... | {
"game_data": {
"answer": "-167",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 3 ⊙ 2 ⊗ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ▽，规则如下：
当x和y的和是奇数时，x ▽ y = abs(x - 3 / 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: 10 + 9 ▽ 6 ▽ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "58.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 + 9 ▽ 6 ▽ 3",
"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 a multiple of 5, x ♢ y = y + y + x + (x);
otherwise, x ♢ y = y / x + 4.
and ⊕, the rules are as follows:
when x is a multiple of 3, x ⊕ y = x ♢ 3 * y - x;
otherwise, x ⊕ y = x + x * y ♢ x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y * y - ... | {
"game_data": {
"answer": "4.06502",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 6 ♢ 9 ◎ 9 ♢ 5",
"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3的倍数时，x ◎ y = 4 - y - x - x；
其他情况下，x ◎ y = x + y + 3。
和 △，规则如下：
实数域上，x △ y = y + 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 ◎ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 9",
"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 the sum of x and y is even, x ♢ y = x - y - 1 / x;
otherwise, x ♢ y = x * x - y * x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y + x + y - y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x - x / y.
The precedence of operatio... | {
"game_data": {
"answer": "-4.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 9 ☆ 4 ♡ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ☆, the rules are as follows:
when y is a multiple of 5, x ☆ y = x + x - y;
otherwise, x ☆ y = y / 4 * 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 insi... | {
"game_data": {
"answer": "47.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 8 % 7 ** 10 ☆ 9",
"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5的倍数时，x ⊙ y = x * abs(y) * 1 + 2 - 5；
其他情况下，x ⊙ y = 1 * y * y ** 4 / x。
和 ▽，规则如下：
当x大于y时，x ▽ y = x + y * y - x + x；
其他情况下，x ▽ y = y * x ** y + y + x。
和 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = (x) ▽ y + 2 + 4 - 3；
其他情况下，x ⊗ y = (x + x * y ⊙ 5) - y。
运算优先级：⊗ > ** > * = / = % > + = - = ⊙ = ▽。
括号具有最高优先级，先计算括号内的... | {
"game_data": {
"answer": "5589",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 4 ⊙ 5 ⊙ 8 ⊗ 2",
"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 = 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 ◇ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-9",
"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 | 定义 ◇，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: 6 ◇ 8 + 5 - 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-40",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 8 + 5 - 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define △, the rules are as follows:
when y is odd, x △ y = y + y + x * x - 3;
otherwise, x △ y = (y - 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 expr... | {
"game_data": {
"answer": "99",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 8 + 3 △ 10",
"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 and y are both odd, x ♡ y = y / y / x + x;
otherwise, x ♡ y = (y + y) * y - x.
and □, the rules are as follows:
on the real number field, x □ y = x * y + 5 ♡ x.
The precedence of operations: □ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the e... | {
"game_data": {
"answer": "283",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 1 □ 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:
on the real number field, x ⊙ y = x * abs(y - x - x) + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = (y + x / 5) + x / y.
and ▽, the rules are as follows:
when y is odd, x ▽ y = 4 / (y) + x * 3 - 1;
otherwise, x ▽ y = 3 * y - x + 3 + y.
The precedence ... | {
"game_data": {
"answer": "20.186667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 2 ⊙ 5 ▽ 9",
"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 3, x ◎ y = (x) - y * x;
otherwise, x ◎ y = x * x + y.
and ⊙, 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 insi... | {
"game_data": {
"answer": "-56",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 3 ⊙ 6",
"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 + y.
and ◎, the rules are as follows:
when y is a multiple of 3, x ◎ y = x + (y / y);
otherwise, x ◎ y = x / y ⊕ x.
and □, the rules are as follows:
when x is a multiple of 5, x □ y = abs(y / x);
otherwise, x □ y = x * y * y.
The prec... | {
"game_data": {
"answer": "0.12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 5 □ 6",
"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 = 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: 5 □ 8 - 4 □ 7
Please fill your ... | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 8 - 4 □ 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 - 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: 10 ◇ 9 ◇ 1 ** 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "86.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◇ 9 ◇ 1 ** 8",
"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 + y.
and ○, the rules are as follows:
when the sum of x and y is even, x ○ y = abs(x + x - y);
otherwise, x ○ y = y * x ☆ x.
The precedence of operations: ☆ > ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expr... | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 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：
实数域上，x ⊗ y = x / 3 + y + x / 2。
和 ○，规则如下：
当x是3的倍数时，x ○ y = y ⊗ y - x；
其他情况下，x ○ y = x + x + y + y。
和 ◇，规则如下：
实数域上，x ◇ y = (x - y) * y ** x - 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: 2 ◇ 7 ⊗ 2 ○ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-189",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 7 ⊗ 2 ○ 6",
"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 and y are both even, x ☆ y = abs(x * x + x) + y;
otherwise, x ☆ y = x - y * x - 5.
and □, the rules are as follows:
when y is a multiple of 5, x □ y = y - y * x - y;
otherwise, x □ y = x - y * y.
The precedence of operations: ☆ > ** > * = / = % > + = - = □。
Parentheses... | {
"game_data": {
"answer": "-58",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 5 □ 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:
when x is even, x ◎ y = x * y * x;
otherwise, x ◎ 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 expression: 6 ◎ 8
Ple... | {
"game_data": {
"answer": "288",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
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