env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define ♡, the rules are as follows:
when the sum of x and y is even, x ♡ y = x - y * y;
otherwise, x ♡ y = y * x - (y).
and ⊙, the rules are as follows:
when y is even, x ⊙ y = x ** x ♡ y;
otherwise, x ⊙ y = (y ** x).
The precedence of operations: ** = ♡ > * = / = % = ⊙ > + = -。
Parentheses have the highest pri... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 1 ♡ 6 - 5",
"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 = 3 * (x * y * x - 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: 9 ▽ 10
Please fill yo... | {
"game_data": {
"answer": "2427",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ⊙，规则如下：
当x是偶数时，x ⊙ y = abs(x * y)；
其他情况下，x ⊙ y = y + x * y。
和 ♡，规则如下：
实数域上，x ♡ y = (y / 4) / x。
和 □，规则如下：
实数域上，x □ y = abs(x + 1 + y)。
运算优先级：** = □ > * = / = % > + = - = ⊙ = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 2 □ 2 ⊙ 5 ⊙ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "61.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 2 □ 2 ⊙ 5 ⊙ 5",
"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:
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 calculate... | {
"game_data": {
"answer": "70756",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♢ 1 ♡ 7 ** 2",
"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 = abs(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 expression: 4
Please fill your fi... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4",
"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:
when x is odd, x ○ y = y - x * y;
otherwise, 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: 4 ○ 2
Pl... | {
"game_data": {
"answer": "-4",
"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x和y的和是奇数时，x ♡ y = x + y + x；
其他情况下，x ♡ y = y - 5 / x。
和 ☆，规则如下：
实数域上，x ☆ y = y * x。
和 ○，规则如下：
当x是5的倍数时，x ○ y = (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: 7 ☆ 7 ♡ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "58.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ☆ 7 ♡ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x * y ** 3 * 5 + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + y - y + x ◎ 5.
The precedence of operations: ** = ◎ > * = / = % > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parenthes... | {
"game_data": {
"answer": "3135",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 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 = 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
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 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y + (x - x) * y.
and ⊗, the rules are as follows:
when y is even, x ⊗ y = y / x + 3 * y;
otherwise, x ⊗ y = (x / y - y).
and ◎, the rules are as follows:
on the real number field, x ◎ y = abs(y) + x * 4 + 5 + y.
The precedence of operations: ... | {
"game_data": {
"answer": "29",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 2 ◎ 8",
"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 = abs(y - x * y - y)。
和 ◇，规则如下：
当y是偶数时，x ◇ y = x + x ⊗ y + x；
其他情况下，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: 4 ◇ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 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：
当x大于y时，x ⊗ y = 2 - 2 - y - x；
其他情况下，x ⊗ y = y * x - y。
和 ▽，规则如下：
实数域上，x ▽ y = x / y ⊗ x。
和 △，规则如下：
实数域上，x △ 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: 4 ▽ 4 / 3 ⊗ 1 △ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 4 / 3 ⊗ 1 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = abs(y * x + 1)。
和 ▽，规则如下：
当x和y的和是奇数时，x ▽ y = (y) ♢ x；
其他情况下，x ▽ y = (x) ♢ y。
和 ⊗，规则如下：
当y是5的倍数时，x ⊗ y = (x / y / x)；
其他情况下，x ⊗ y = y / 4 ▽ 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 / 6 ♢ 10 / 5 ⊗ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "129.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 1 / 6 ♢ 10 / 5 ⊗ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": nu... |
logic-v2 | Define ⊙, the rules are as follows:
when x is less than y, x ⊙ y = 5 + x * y + x;
otherwise, x ⊙ y = 2 * x * y + 4.
and ◎, the rules are as follows:
when x is a multiple of 5, x ◎ y = abs(y ** x) + y;
otherwise, x ◎ y = 3 - x ⊙ x * y.
and △, the rules are as follows:
when y is a multiple of 3, x △ y = y + x +... | {
"game_data": {
"answer": "-2693",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 7 ◎ 7 + 6 ⊙ 6",
"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 even, x ♢ y = 2 / x - (x + y);
otherwise, x ♢ y = y - x - 5 - x * y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x - y + abs(y).
and △, the rules are as follows:
when y is even, x △ y = x * y - 3;
otherwise, x △ y = x * x - (x + y) + x.
The ... | {
"game_data": {
"answer": "-70",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 2 ♢ 3 ☆ 4",
"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 = 3 * x * y - y.
and △, the rules are as follows:
on the real number field, x △ y = y ♢ x / x * y.
and ⊗, the rules are as follows:
when x is odd, x ⊗ y = y ♢ x;
otherwise, x ⊗ y = x + x + y.
The precedence of operations: ⊗ > ** = ♢ = △ > * = /... | {
"game_data": {
"answer": "609",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 7 + 10 △ 6 ⊗ 2",
"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 - y。
和 ☆，规则如下：
实数域上，x ☆ y = x ♢ y - 1。
和 ◎，规则如下：
当y是5的倍数时，x ◎ y = x + x * y - y；
其他情况下，x ◎ y = (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: 2 % 5 ◎ 1 ♢ 4 ☆ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 % 5 ◎ 1 ♢ 4 ☆ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = 5 + y + 3 - 5 * x。
和 □，规则如下：
实数域上，x □ y = x + (x * y * 1) ♡ 4。
和 ◇，规则如下：
实数域上，x ◇ y = abs(5 * 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 ♡ 5 □ 9 ◇ 1 - 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-497",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 5 □ 9 ◇ 1 - 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y + x * (x - x + y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = x - x ♡ (y + y + y).
The precedence of operations: ▽ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression inside the parent... | {
"game_data": {
"answer": "3",
"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": ... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y * x - y - x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4
Please fill your final an... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4",
"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: 3 ○ 4
Please fill your final an... | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ♢，规则如下：
当y是3的倍数时，x ♢ y = y * x * x；
其他情况下，x ♢ y = y * x。
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 * 3)。
运算优先级：** = ⊙ > * = / = % > + = - = ♢ = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ⊗ 2 ♢ 2 ⊗ 2 ⊙ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "648",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 2 ♢ 2 ⊗ 2 ⊙ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = x + y / x.
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 % 5 ○ 8
Please fill your fina... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 % 5 ○ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ◇，规则如下：
当x小于y时，x ◇ y = y * 2 * x；
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: 5 ◇ 9 + 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "97",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 9 + 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = 2 + abs(x + y) / 3。
和 ♢，规则如下：
实数域上，x ♢ y = x - x + y ⊙ y。
和 ♡，规则如下：
当x和y的和是奇数时，x ♡ y = x ** 4 ⊙ y * y；
其他情况下，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 ♢ 2 ♡ 5 ⊙ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 2 ♡ 5 ⊙ 3",
"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) - 3.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + (y).
The precedence of operations: ⊙ > ** > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "32",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 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等于y时，x ◎ y = 2 - y * x；
其他情况下，x ◎ y = 2 ** y + x - y。
和 ⊕，规则如下：
当x是奇数时，x ⊕ y = x ◎ y；
其他情况下，x ⊕ y = x - y + y * y。
运算优先级：◎ > ** > * = / = % > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 * 6 ** 1 ◎ 2 ⊕ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1554",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 * 6 ** 1 ◎ 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 y is odd, x ♡ y = y * y - y - y - x;
otherwise, x ♡ y = y * y - x - y / x.
and ◇, the rules are as follows:
when x is equal to y, x ◇ y = y ♡ x / y - y / y;
otherwise, x ◇ y = x ♡ x + y * x.
The precedence of operations: ** > * = / = % = ♡ > + = - = ◇。
Parentheses have t... | {
"game_data": {
"answer": "-35",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 5 ◇ 8 ♡ 1",
"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 = (y) + x；
其他情况下，x ◎ y = abs(x - 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: 2 ◎ 4 □ 10 / 4
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 □ 10 / 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = 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: 6 ◇ 4 % 1 % 7
Please fill y... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 4 % 1 % 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 = x - y - 1 + y。
运算优先级：** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 △ 6 - 2 - 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 6 - 2 - 1",
"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: 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的和是偶数时，x ☆ y = y - 5 + x；
其他情况下，x ☆ y = y * 4 + x + 5。
和 □，规则如下：
实数域上，x □ y = 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: 7 ☆ 3 / 10 □ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ☆ 3 / 10 □ 7",
"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 = y + x * 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: 1 ◎ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◎ 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 = y + x.
and ♡, the rules are as follows:
when x and y are both even, x ♡ y = 2 - x - y + x;
otherwise, x ♡ y = x - y - y + 2.
and ◎, the rules are as follows:
on the real number field, x ◎ y = (x * y) / 5 - x.
The precedence of operations: ** ... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 5 ♡ 8",
"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 - x + y.
and ◇, the rules are as follows:
when x and y are both odd, x ◇ y = 1 - abs(x ** y);
otherwise, x ◇ y = x ** y / x * x + y.
The precedence of operations: ** > * = / = % = ⊕ = ◇ > + = -。
Parentheses have the highest priority, ... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 8 ⊕ 8",
"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 * x + x - y.
and ⊙, the rules are as follows:
when x and y are both odd, x ⊙ y = y □ y - (y ** x);
otherwise, x ⊙ y = x □ (1 + x ** y).
The precedence of operations: ⊙ > ** > * = / = % = □ > + = -。
Parentheses have the highest priority, and t... | {
"game_data": {
"answer": "-78100",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 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 5, x ▽ y = y + x * 4 * 5;
otherwise, x ▽ y = x * (y / y + 2).
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the ... | {
"game_data": {
"answer": "24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 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 y is even, x ♡ y = x + 2 + y;
otherwise, x ♡ y = x - y - x.
and □, the rules are as follows:
when y is a multiple of 5, x □ y = x ** y;
otherwise, x □ y = x / y + y.
The precedence of operations: □ > ♡ > ** > * = / = % > + = -。
Parentheses have the highest priority, and ... | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 6 ♡ 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:
on the real number field, 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 value of the expression: 4 - 2 ** 5 ◇ 5
Please f... | {
"game_data": {
"answer": "-135",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 - 2 ** 5 ◇ 5",
"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 * y / y * y + x.
and ○, the rules are as follows:
when x is equal to y, x ○ y = y ◎ y / x + x;
otherwise, x ○ y = x - x / x + x * y.
The precedence of operations: ** > * = / = % = ○ > + = - = ◎。
Parentheses have the highest priority, and the ... | {
"game_data": {
"answer": "51",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = (1 ** x) * 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: 5 △ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x - 2 + y - 3。
和 ○，规则如下：
实数域上，x ○ y = x + x + x + y / 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: 3 ⊕ 2 ○ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊕ 2 ○ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ◎, the rules are as follows:
when x is greater than y, x ◎ y = y / x + y;
otherwise, x ◎ y = 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 inside the pa... | {
"game_data": {
"answer": "1.96875",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 / 7 ◎ 4 ○ 1",
"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 + y.
and □, the rules are as follows:
when x is equal to y, x □ y = x * (y + 2) + y;
otherwise, x □ y = x * y - y / y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x - y - x ⊙ x.
The precedence of operations: □ > ♡... | {
"game_data": {
"answer": "120",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 7 ⊙ 6 ♡ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
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: 6 ○ 10 * 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "576",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 10 * 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = y + x + x ** y + x.
and ♢, the rules are as follows:
when x is even, x ♢ y = 2 ** 3 - (x + y - 2);
otherwise, x ♢ y = (y + x) ○ y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y - 2 ♢ y + x.
The precedence of operations:... | {
"game_data": {
"answer": "125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 5 ⊗ 7 ○ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ♡，规则如下：
当x和y都是偶数时，x ♡ y = y - (x + x)；
其他情况下，x ♡ y = (y) * x。
和 ⊙，规则如下：
当x是偶数时，x ⊙ y = 4 - (x + y * x - x)；
其他情况下，x ⊙ y = x ♡ y - y - (y)。
运算优先级：** = ♡ > * = / = % = ⊙ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ♡ 8 ** 5 ⊙ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-9212",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 8 ** 5 ⊙ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x - 2 * y。
和 ▽，规则如下：
当x是3的倍数时，x ▽ y = x / abs(y) * y；
其他情况下，x ▽ y = x / y / (x)。
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: 1 ▽ 9 ○ 7 ⊙ 7 * 4 ▽ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 9 ○ 7 ⊙ 7 * 4 ▽ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y - (x * x + 3) * 2.
and ⊕, the rules are as follows:
when y is even, x ⊕ y = x - x / y + y ☆ x;
otherwise, x ⊕ y = x * y / 1 ☆ 1 - 4.
The precedence of operations: ** = ☆ > * = / = % > + = - = ⊕。
Parentheses have the highest priority, and the ... | {
"game_data": {
"answer": "-190.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊕ 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：
实数域上，x △ y = abs(x + y)。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 / 3 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 / 3 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = 5 - x + x * y ** x.
and ⊙, the rules are as follows:
when x is odd, x ⊙ y = abs(y + y - x);
otherwise, x ⊙ y = y / x - x.
The precedence of operations: ** > * = / = % = □ > + = - = ⊙。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "52481",
"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_... |
logic-v2 | 定义 △，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: 7 △ 2 △ 8 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1296",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 2 △ 8 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 △，规则如下：
当x是偶数时，x △ y = abs(y * 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: 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ⊙，规则如下：
当y是奇数时，x ⊙ y = x + y；
其他情况下，x ⊙ y = x * x / y * 5。
和 ☆，规则如下：
实数域上，x ☆ y = y / x ⊙ y。
和 △，规则如下：
当x和y的和是偶数时，x △ y = 1 * (y) + x；
其他情况下，x △ y = 1 ** x * 5 / 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 ☆ 5 △ 2 ⊙ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5.425347",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 5 △ 2 ⊙ 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 equal to y, x ○ y = y + x + x;
otherwise, 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 ○... | {
"game_data": {
"answer": "28",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 7 + 8 + 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ◇, the rules are as follows:
when y is a multiple of 3, x ◇ y = y ** (1 * x);
otherwise, x ◇ y = (2 - x + y / 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 t... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 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 the sum of x and y is odd, x ⊕ y = x * y - x / y;
otherwise, x ⊕ y = y / y - x / y - (y).
and □, the rules are as follows:
on the real number field, x □ y = x + 2 - 2 - y * 3.
and ♡, the rules are as follows:
when x is even, x ♡ y = y * (y + x);
otherwise, x ♡ y = x * ... | {
"game_data": {
"answer": "-294.714286",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 7 □ 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 greater than y, x ◇ y = 5 - abs(5 ** y + x) + y;
otherwise, x ◇ y = 2 * y / 4 * x - 1.
The precedence of operations: ** > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the va... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ◎，规则如下：
当x大于y时，x ◎ y = y * x ** 3 * 1；
其他情况下，x ◎ y = x * abs(5) ** y - y。
和 ⊕，规则如下：
当y是3的倍数时，x ⊕ y = y ** y / y - x；
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: 8 ⊕ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊕ 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 - y + x。
和 ◎，规则如下：
实数域上，x ◎ y = y / y + x。
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: 4 ◎ 7 ◇ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 7 ◇ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ○, the rules are as follows:
when x and y are both odd, x ○ y = x - 1 + y;
otherwise, 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... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 7 ○ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = (y - x + x ** y - y);
otherwise, x ▽ y = abs(1 * y * y + x) + 1.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calcula... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"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:
when x is greater than y, x ◇ y = x - x + y * x;
otherwise, x ◇ y = 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 exp... | {
"game_data": {
"answer": "0.055556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 2 / 9 ◇ 2",
"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 = x - y - y * 4；
其他情况下，x ⊗ y = y + 3 * x - x。
和 ⊙，规则如下：
实数域上，x ⊙ y = (1 ⊗ y) + 5 + 3 * x。
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 ◎ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "41",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊙ 4 ◎ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ▽，规则如下：
当x和y的和是奇数时，x ▽ y = y / 4 * y - x / (y)；
其他情况下，x ▽ y = y ** 2 * 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: 8 ▽ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4.65",
"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:
on the real number field, x ⊙ y = y - y - x - y.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x - y + x ** (x).
and ♢, the rules are as follows:
when y is odd, x ♢ y = (y * y) ** x * x;
otherwise, x ♢ y = y + x + 2 - x.
The precedence of operations: ⊙ > ... | {
"game_data": {
"answer": "252",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 2 ♡ 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 = 3 - (y) / x * y。
和 △，规则如下：
实数域上，x △ y = x + x * x ♢ y。
和 ○，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: 4 ○ 8 △ 8 ♢ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-27.945873",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 8 △ 8 ♢ 9",
"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 - x.
and ⊗, the rules are as follows:
when x is less than y, x ⊗ y = (x □ y - x - x);
otherwise, x ⊗ y = y - 1 + y * y □ x.
The precedence of operations: ** = ⊗ > * = / = % > + = - = □。
Parentheses have the highest priority, and the e... | {
"game_data": {
"answer": "-5.307692",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 10 □ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | Define ♢, the rules are as follows:
when x is a multiple of 5, x ♢ y = y + 3 * (x + x);
otherwise, x ♢ y = y * x - y - (y).
and ⊕, the rules are as follows:
when the sum of x and y is even, x ⊕ y = y * (y ♢ x);
otherwise, x ⊕ y = y - x * y + x.
and □, the rules are as follows:
on the real number field, x □ y = ... | {
"game_data": {
"answer": "31",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 2 □ 1 % 3 ♢ 1 * 8",
"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3的倍数时，x □ y = x + x + y - y；
其他情况下，x □ y = y / 5 * x - x。
和 ⊕，规则如下：
当x和y都是偶数时，x ⊕ y = x □ y - y + 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: 4 - 8 □ 5 ⊕ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 - 8 □ 5 ⊕ 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x和y都是偶数时，x ○ y = y / y * (x * x - x)；
其他情况下，x ○ y = abs(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: 2 ○ 3 - 10 + 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 3 - 10 + 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 = y ** 2 * x * y。
和 ◇，规则如下：
当x是奇数时，x ◇ y = x - x + y；
其他情况下，x ◇ y = (y / x) ▽ y ** y - x。
和 ○，规则如下：
实数域上，x ○ y = (x - 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: 9 ▽ 7 ◇ 7 ◇ 7 + 8 ○ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3151",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 7 ◇ 7 ◇ 7 + 8 ○ 4",
"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(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: 5 ◇ 2 - 8 * 1
Please f... | {
"game_data": {
"answer": "-1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 2 - 8 * 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ◎，规则如下：
当x和y的和是偶数时，x ◎ y = (x + x - y * x)；
其他情况下，x ◎ y = x - y + 2 + y。
和 ♢，规则如下：
当x小于y时，x ♢ y = y + x + y ◎ x；
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: 8 % 4 / 6 ◎ 10 ♢ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 % 4 / 6 ◎ 10 ♢ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
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 = x * y + x.
The precedence of operations: ** > * = / = % > + = - = □ = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated fi... | {
"game_data": {
"answer": "264",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 9 + 7 ○ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = (x) - 3 + y.
and ○, the rules are as follows:
when x is less than y, x ○ y = 2 ** x * y;
otherwise, x ○ y = y * x ⊙ 5.
and △, the rules are as follows:
on the real number field, x △ y = y * x / x.
The precedence of operations: ** = ⊙ = ○ = △ ... | {
"game_data": {
"answer": "77",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 9 ○ 7",
"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 ** x - y + abs(x + x).
and ◇, the rules are as follows:
when x is equal to y, x ◇ y = y ♡ x + 5 - y;
otherwise, x ◇ y = x * abs(y).
The precedence of operations: ♡ > ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the e... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 3 * 6 ♡ 2 % 3",
"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 = x - y / y。
和 △，规则如下：
实数域上，x △ y = y / y - x。
运算优先级：♡ > ** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ♡ 8 * 2 △ 8 ♡ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 8 * 2 △ 8 ♡ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
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 x and y are both even, x △ y = y / (x + x);
otherwise, x △ y = y * abs(x) + x.
The precedence of operations: △ > ** > * = / = % = ◎ > + = -。
Parentheses have the highest priority, and the express... | {
"game_data": {
"answer": "64",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 4 △ 7",
"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 + 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: 3
Please fill your final answer... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y + x * 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": nu... |
logic-v2 | 定义 □，规则如下：
当x和y的和是奇数时，x □ y = 4 + y * x；
其他情况下，x □ y = 3 - y - x。
和 ◇，规则如下：
实数域上，x ◇ y = 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 □ 5 ◇ 6 - 6 - 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 □ 5 ◇ 6 - 6 - 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 ⊙，规则如下：
当y是偶数时，x ⊙ y = (x) - x + y；
其他情况下，x ⊙ y = x / y - 1。
和 ◎，规则如下：
当x是奇数时，x ◎ y = x * y ⊙ x；
其他情况下，x ◎ y = x * y ⊙ y。
和 ⊗，规则如下：
实数域上，x ⊗ y = x * 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: 2 ⊙ 6 ⊙ 10 ⊗ 3 ◎ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "72",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 6 ⊙ 10 ⊗ 3 ◎ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x + y / y * y.
and ○, the rules are as follows:
when x and y are both odd, x ○ y = y * x - 2 ◎ x;
otherwise, x ○ y = abs(y) + x + y.
The precedence of operations: ◎ > ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the ex... | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 5 ◎ 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是奇数时，x ♡ y = y * x + x；
其他情况下，x ♡ y = x * 5 - y。
和 □，规则如下：
当x小于y时，x □ y = x / y + 1 ♡ y；
其他情况下，x □ y = x ♡ 5 + 5 - 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 □ 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 ♡ 10 □ 3",
"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 * y - x - 3.
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: 9 ○ 10
Please fill your fin... | {
"game_data": {
"answer": "88",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 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是偶数时，x ⊗ y = y + x；
其他情况下，x ⊗ y = y - x + y。
和 ○，规则如下：
实数域上，x ○ y = y ⊗ x * x。
和 △，规则如下：
当y是5的倍数时，x △ y = y - x ** x；
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: 4 ○ 3 ⊗ 5 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "61",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 3 ⊗ 5 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define □, the rules are as follows:
when x is less than y, x □ y = x + y + y + y - x;
otherwise, x □ y = x - x - x * y * y.
and ⊙, the rules are as follows:
when x is odd, x ⊙ y = x + x / x + y;
otherwise, x ⊙ y = y * y □ y / y * x.
The precedence of operations: ⊙ > ** = □ > * = / = % > + = -。
Parentheses have ... | {
"game_data": {
"answer": "-0.052288",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 / 9 ⊙ 7 □ 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 = 3 - 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 / 5 △ 6 △ 10
Please fill ... | {
"game_data": {
"answer": "83",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 / 5 △ 6 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x + y + x * y * y.
and ☆, the rules are as follows:
when the sum of x and y is odd, x ☆ y = x ♢ y + y + y + 5;
otherwise, x ☆ y = (x / x - x + x) + y.
and ⊙, the rules are as follows:
when y is a multiple of 3, x ⊙ y = 5 - x / y - x ♢ x;
othe... | {
"game_data": {
"answer": "205.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ☆ 7 ⊙ 5 ♢ 9",
"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 = 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 ▽ 5 / 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ▽ 5 / 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 □，规则如下：
当y是3的倍数时，x □ y = (x) - x * y；
其他情况下，x □ y = y / 5 * (x + y * x)。
和 ☆，规则如下：
当x是奇数时，x ☆ y = 3 □ 1 - x / y - 1；
其他情况下，x ☆ y = (x □ 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: 3 ☆ 7 □ 3 ** 2 / 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.020522",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 7 □ 3 ** 2 / 9",
"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 * y + x.
and △, the rules are as follows:
when y is even, x △ y = y / y ☆ x;
otherwise, x △ y = (y + x - x).
and ◎, the rules are as follows:
when the sum of x and y is odd, x ◎ y = y ☆ y - x;
otherwise, x ◎ y = x △ y.
The precedence of o... | {
"game_data": {
"answer": "0.047619",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 9 △ 4 ☆ 4 ◎ 3",
"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3的倍数时，x ◇ y = x - x / (x + y)；
其他情况下，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: 2 ◇ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "30",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 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 = 3 - y - x + y。
和 ▽，规则如下：
实数域上，x ▽ y = y * y / x。
和 □，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: 7 □ 6 ♢ 6 ▽ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.175978",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 6 ♢ 6 ▽ 3",
"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 + y - y / x / x.
and ⊕, 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 = y + y - 2 * x + y.
The precedence of operations: ⊕ > ** > * = / = % = ⊙ > + ... | {
"game_data": {
"answer": "25.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 / 1 □ 5 ⊕ 5 % 7 ⊙ 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 = (y) - x + y.
and ○, the rules are as follows:
on the real number field, x ○ y = (2) + 1 - y + y + x.
The precedence of operations: ** > * = / = % = □ = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is... | {
"game_data": {
"answer": "-55",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ** 2 □ 3 ○ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ▽，规则如下：
当y是3的倍数时，x ▽ 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 ▽ 8 - 10 % 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "45",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 8 - 10 % 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)。
和 ▽，规则如下：
当x等于y时，x ▽ y = x + x + x ♢ y；
其他情况下，x ▽ y = x ♢ y - 5 * 1。
和 □，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: 5 ▽ 3 □ 7 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.349206",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 3 □ 7 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
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