env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define △, the rules are as follows:
when x and y are both odd, x △ y = y + x;
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 inside ... | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 % 9 △ 1 ◇ 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 the sum of x and y is odd, x ♢ y = x * x / y - y;
otherwise, x ♢ y = y - y * y * x.
and □, the rules are as follows:
when y is a multiple of 5, x □ y = x ♢ x * 5 + y;
otherwise, x □ y = x * y ** 4.
and ☆, the rules are as follows:
on the real number field, x ☆ y = 1 * ... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 2 ♢ 4",
"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 = y - x - y - y.
and ○, the rules are as follows:
on the real number field, x ○ y = x + y * y + y.
The precedence of operations: ○ > ** > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "-24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 2 ☆ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ◎，规则如下：
当x小于y时，x ◎ y = x + x - y * x * x；
其他情况下，x ◎ y = y + 5 + y + x + y。
和 ♡，规则如下：
实数域上，x ♡ y = x + y - x + y ◎ y。
运算优先级：** = ♡ > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ** 7 ♡ 9 ◎ 4 % 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "58",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ** 7 ♡ 9 ◎ 4 % 3",
"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) / 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: 4 ▽ 8 * 8
Please fill you... | {
"game_data": {
"answer": "-63.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 8 * 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ♢，规则如下：
当x大于y时，x ♢ y = x * y - 3 - y；
其他情况下，x ♢ y = y + x + x + 5 + x。
和 ▽，规则如下：
实数域上，x ▽ y = 1 ** 3 ♢ x + x + y。
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: 9 ▽ 9 ☆ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "35.885714",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 9 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x + y - x.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8
Please fill your final answer... | {
"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 | 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: 8 ◇ 8
Please fill your... | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 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 = (y * 1 * x).
and ◇, the rules are as follows:
when x and y are both even, x ◇ y = x ◎ (y);
otherwise, x ◇ y = (y + x - y).
The precedence of operations: ** = ◇ > * = / = % > + = - = ◎。
Parentheses have the highest priority, and the expression i... | {
"game_data": {
"answer": "28",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◇ 10 % 8 ** 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 less than y, x ⊗ y = (y + x * y) / x;
otherwise, x ⊗ y = x * x * y.
and △, the rules are as follows:
when x is less than y, x △ y = 4 / y ⊗ (1 + x);
otherwise, x △ y = y + x + y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = x △ y.
The precede... | {
"game_data": {
"answer": "6084",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 8 ◎ 7 ⊗ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ◇, the rules are as follows:
when the sum of x and y is even, x ◇ y = x - y * x;
otherwise, 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 t... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 9 ◇ 7 % 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y / y + x.
and ○, the rules are as follows:
on the real number field, x ○ y = 1 - y * x + y.
The precedence of operations: ☆ > ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calcula... | {
"game_data": {
"answer": "-15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ◇, the rules are as follows:
when y is a multiple of 5, x ◇ y = 1 - x - x ** y;
otherwise, x ◇ y = x + y - y ** x.
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the ... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 % 9 ◇ 10 ** 10",
"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 = y - y + y + x;
otherwise, x ♡ y = y + x - y * x.
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 ... | {
"game_data": {
"answer": "31",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 6 □ 2",
"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 = y + x + x - 2.
and □, the rules are as follows:
on the real number field, x □ y = abs(y - x) + x.
and ♡, the rules are as follows:
when y is a multiple of 3, x ♡ y = y * x;
otherwise, x ♡ y = x + x □ y.
The precedence of operations: ** = □ > ... | {
"game_data": {
"answer": "270",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 10 ♡ 10 ⊙ 9",
"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 + x.
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... | {
"game_data": {
"answer": "0.16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 / 9 ♢ 9 □ 7",
"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都是偶数时，x ○ y = 3 - x - y - 1 * 1；
其他情况下，x ○ y = (x + 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: 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x + y + 4.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 ◇ 7 + 2 - 5
Please fill your ... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 7 + 2 - 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ◇，规则如下：
当x是3的倍数时，x ◇ y = x ** y + y * x；
其他情况下，x ◇ y = 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 ◇ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ○, the rules are as follows:
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: 7
Please fill your final an... | {
"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 | 定义 ♢，规则如下：
当x和y的和是奇数时，x ♢ y = y ** x / x；
其他情况下，x ♢ y = abs(y + y) + x。
和 ○，规则如下：
当y是偶数时，x ○ y = y + (y) * x；
其他情况下，x ○ y = 5 * x + y。
和 ◎，规则如下：
当x等于y时，x ◎ y = x + (y * y)；
其他情况下，x ◎ y = x - (2 - 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 ○ 3 ◎ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 3 ◎ 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 odd, x △ y = x + y;
otherwise, x △ y = x - y * x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6
... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define △, the rules are as follows:
when x and y are both odd, x △ y = 5 * 3 * 1 * x + y;
otherwise, x △ y = x - 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 ... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ◇, the rules are as follows:
when y is odd, x ◇ y = 5 / y - 5 - x;
otherwise, x ◇ y = x + x - x * y.
The precedence of operations: ** > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2
... | {
"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:
when x is odd, x ♡ y = x + x + y * y ** 5;
otherwise, x ♡ y = abs(x * y + x - x * y).
and ☆, the rules are as follows:
on the real number field, x ☆ y = x - (x * y * y).
The precedence of operations: ♡ > ☆ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the... | {
"game_data": {
"answer": "-198",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 10 ♡ 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 - (x - y)。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ▽ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "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 = x - abs(x / y)。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ○ 1 % 9 ○ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 1 % 9 ○ 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 odd, x ○ y = 5 + y * (x + y);
otherwise, 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 exp... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 7 - 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = y + y * x;
otherwise, x ⊗ y = y + abs(x).
and ◇, the rules are as follows:
on the real number field, x ◇ y = 1 / y - x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = x - 5 - y * 3.
The precedence of operations: ⊗ > ** = ◇... | {
"game_data": {
"answer": "-109.7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 - 2 ⊗ 7 ☆ 6 ** 2 ◇ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x * (y)。
和 ⊕，规则如下：
当x和y都是奇数时，x ⊕ y = x + y + x - y；
其他情况下，x ⊕ y = y ♢ x * x / y。
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: 5 ⊕ 10 ♢ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "200",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 10 ♢ 8",
"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 * x + y + 1.
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 inside the parentheses is calcula... | {
"game_data": {
"answer": "4700",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 8 ♢ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ○，规则如下：
当x等于y时，x ○ y = 2 * x / y - 4；
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 ○ 1 + 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8201",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ** 4 ○ 1 + 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
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 = x + 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: 9 + 4 + 7 ◇ 7 ☆ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "136",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 + 4 + 7 ◇ 7 ☆ 2",
"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 + 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: 10 △ 4 △ 1
Please fill yo... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 4 △ 1",
"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 = x * 5 + y。
和 ◇，规则如下：
当x是5的倍数时，x ◇ y = y + x；
其他情况下，x ◇ y = y ⊙ 2 - x。
和 ⊗，规则如下：
当y是奇数时，x ⊗ y = x * y + y；
其他情况下，x ⊗ y = x ** y ◇ x。
运算优先级：⊙ > ** > * = / = % > + = - = ◇ = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ⊗ 9 ◇ 3 ⊙ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "23",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊗ 9 ◇ 3 ⊙ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x * 1 + 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 △ 10
Please fill your final a... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 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：
实数域上，x ◇ y = y - x ** y * 2 - (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: 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊗, the rules are as follows:
when x is less than y, x ⊗ y = x / x + y + y;
otherwise, x ⊗ y = y * 4 * x - y * x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y + y - x - y + y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (y / x * y) ♡ x - y.
The precedence of ... | {
"game_data": {
"answer": "-25.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ☆ 5 ♡ 6 - 3 ♡ 4 ⊗ 9",
"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.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 - 2 △ 3
Please fill your fina... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 2 △ 3",
"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 a multiple of 5, 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 expressi... | {
"game_data": {
"answer": "0",
"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,
"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 - y * y - 5.
and ◎, the rules are as follows:
when y is a multiple of 5, x ◎ y = 5 + x / 4 - y;
otherwise, x ◎ y = x * y.
The precedence of operations: □ > ** > * = / = % > + = - = ◎。
Parentheses have the high... | {
"game_data": {
"answer": "100.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 5 % 5 □ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 □，规则如下：
当y是偶数时，x □ y = 2 * x / y；
其他情况下，x □ 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: 2 ◎ 1 □ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 1 □ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = x / 5 - x + y * 5.
and ◎, the rules are as follows:
on the real number field, x ◎ y = x + x * y ♡ x * x.
The precedence of operations: ♡ > ** = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parenthese... | {
"game_data": {
"answer": "17.04",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 9 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ♢，规则如下：
当x和y都是奇数时，x ♢ y = (2 / y / x)；
其他情况下，x ♢ y = y + x。
和 ○，规则如下：
实数域上，x ○ y = y + x * (x)。
和 ◎，规则如下：
当x和y的和是奇数时，x ◎ y = y * y - x；
其他情况下，x ◎ y = y + abs(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 ◎ 9 ○ 7 ○ 7 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7746.057143",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 9 ○ 7 ○ 7 ♢ 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 - y - x.
and ○, the rules are as follows:
when the sum of x and y is odd, x ○ y = y + x - y;
otherwise, x ○ y = y + x.
and ⊙, the rules are as follows:
when x and y are both odd, x ⊙ y = y - x + x;
otherwise, x ⊙ y = x - y ○ x.
The preced... | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 10 ⊙ 2 ○ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = (y - 2 * x)。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ▽, the rules are as follows:
when x is odd, x ▽ y = y + x - y;
otherwise, x ▽ y = y * abs(x * x) * x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = y - x - x - y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (y) + 1 - x + y.
The precedence of operations: ☆ > ** ... | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 6 ☆ 8 ♢ 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y是5的倍数时，x ▽ y = y + x + y；
其他情况下，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: 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = y + y + 2 + x。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ○ 2 ○ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 2 ○ 5",
"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 y is a multiple of 3, x ○ y = x * y / x - 3;
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 expres... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x * y - y。
和 ○，规则如下：
实数域上，x ○ y = abs(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 ○ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 4",
"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 greater than y, x △ y = y + abs(5 * 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 ... | {
"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和y的和是奇数时，x ⊗ y = x * y + y + y；
其他情况下，x ⊗ y = y + y / y - x * y。
和 ○，规则如下：
当y是偶数时，x ○ y = abs(x * y * x) - y + x；
其他情况下，x ○ y = x - y ⊗ x * y * y。
和 ⊙，规则如下：
当x是偶数时，x ⊙ y = x - (y - 2) / x；
其他情况下，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: 9... | {
"game_data": {
"answer": "-3872",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 8 ○ 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 - 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-120",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 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 = x ** y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * y - x.
and ☆, the rules are as follows:
when y is odd, x ☆ y = x ** y ** abs(y);
otherwise, x ☆ y = y - x ⊕ y.
The precedence of operations: ** = ◎ > * = / = % = ⊕... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 1 ⊕ 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：
当x是偶数时，x ♢ y = y * y - x；
其他情况下，x ♢ y = 4 / x - 5 - y。
和 ⊗，规则如下：
当x等于y时，x ⊗ y = x + y + y - y；
其他情况下，x ⊗ y = y - y + x ♢ x。
和 ◎，规则如下：
实数域上，x ◎ 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: 5 ⊗ 10 ◎ 8 ♢ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-9.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 10 ◎ 8 ♢ 6",
"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 ** abs(x) + 4 + y。
和 ♢，规则如下：
实数域上，x ♢ y = 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 % 8 □ 7 ♢ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 % 8 □ 7 ♢ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x + x + y。
和 □，规则如下：
实数域上，x □ y = x - y / x。
运算优先级：** > * = / = % = ☆ > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ☆ 8 □ 3 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "25.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 8 □ 3 ☆ 7",
"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 odd, x ⊗ y = y - x - 4 - y;
otherwise, x ⊗ y = abs(3) + y / x - x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = 1 - x * y ⊗ x.
and ○, the rules are as follows:
when the sum of x and y is even, x ○ y = y + x;
otherwise, x ○ y = y +... | {
"game_data": {
"answer": "0.916667",
"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,
"nesti... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y / x - 1。
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 ◇ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 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 odd, x ▽ y = x + y + 4;
otherwise, x ▽ y = 2 + 5 + y * x.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ▽ 9
... | {
"game_data": {
"answer": "25",
"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：
当y是偶数时，x □ y = x - 3 + y - 4 - x；
其他情况下，x □ y = x - y + y + y。
和 ♢，规则如下：
当x小于y时，x ♢ y = x □ x - y + y - y；
其他情况下，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: 7 ♢ 4 □ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 4 □ 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 even, x ◎ y = x * abs(y) * x + y;
otherwise, x ◎ y = 4 - x / y.
and ⊗, the rules are as follows:
when x is less than y, x ⊗ y = x + 5 / y;
otherwise, x ⊗ y = x + y.
The precedence of operations: ◎ > ** = ⊗ > * = / = % > + = -。
Parentheses have the highes... | {
"game_data": {
"answer": "12.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 * 3 ◎ 4 ⊗ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 ☆，规则如下：
当y是奇数时，x ☆ y = x * y * x；
其他情况下，x ☆ y = x + x + y。
和 ♡，规则如下：
实数域上，x ♡ y = y - x * abs(x)。
运算优先级：♡ > ** > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ☆ 1 ♡ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 1 ♡ 5",
"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 * y / y;
otherwise, x □ y = x * y - abs(5) / 2.
and ☆, the rules are as follows:
when x is less than y, x ☆ y = y + y + y □ x;
otherwise, x ☆ y = x + 5 ** y - x.
The precedence of operations: ** = ☆ > * = / = % > + = - = □。
Paren... | {
"game_data": {
"answer": "100.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 2 ☆ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y * x + x。
和 ☆，规则如下：
实数域上，x ☆ y = x / y ⊙ x。
和 △，规则如下：
当y是偶数时，x △ y = 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: 2 ⊙ 10 ⊙ 7 ☆ 5 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-68724.15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 10 ⊙ 7 ☆ 5 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ⊙，规则如下：
当x是3的倍数时，x ⊙ y = x * x + x - y；
其他情况下，x ⊙ y = (y - y + x)。
和 ◎，规则如下：
实数域上，x ◎ y = y ⊙ x + x - x。
和 △，规则如下：
当y是偶数时，x △ y = y ⊙ 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: 1 ⊙ 1 △ 7 ◎ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊙ 1 △ 7 ◎ 3",
"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 * 5 - 4.
and ☆, the rules are as follows:
when x is a multiple of 3, x ☆ y = y * y * x ♢ x;
otherwise, x ☆ y = y - y - x ♢ y.
The precedence of operations: ** = ♢ = ☆ > * = / = % > + = -。
Parentheses have the highest priority, and the exp... | {
"game_data": {
"answer": "-4644",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 6 ♢ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x + y + 3 * 4.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 - 2 ◇ 7
Please fill your ... | {
"game_data": {
"answer": "-14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 - 2 ◇ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = y * x + y。
和 ◎，规则如下：
实数域上，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: 6 ♡ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "49",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x + x * y / 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 * 6 ▽ 9
Please fill your ... | {
"game_data": {
"answer": "84",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 * 6 ▽ 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y是偶数时，x ♢ y = 3 / x - y；
其他情况下，x ♢ y = x / y。
和 ⊕，规则如下：
实数域上，x ⊕ y = x * y - x。
和 ♡，规则如下：
当x和y都是奇数时，x ♡ y = x - y + x；
其他情况下，x ♡ y = (x ♢ y) - x。
运算优先级：⊕ > ** = ♢ = ♡ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ♢ 8 ⊕ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-63",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 8 ⊕ 9",
"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.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ▽ 9 / 3
Please fill your final an... | {
"game_data": {
"answer": "3.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 9 / 3",
"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小于y时，x ▽ y = y + 1 * x；
其他情况下，x ▽ y = 1 + y * 2 + x。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ▽ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 3",
"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的和是奇数时，x ☆ y = y + x；
其他情况下，x ☆ y = x - y + y。
和 ⊗，规则如下：
当x是5的倍数时，x ⊗ y = y ☆ x - y；
其他情况下，x ⊗ y = x + x ☆ y。
运算优先级：** = ☆ > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ** 1 ☆ 3 ⊗ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ** 1 ☆ 3 ⊗ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = (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: 9 / 9 ◇ 3
Please fill your fi... | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 / 9 ◇ 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x是5的倍数时，x ⊙ y = x - y + x * y；
其他情况下，x ⊙ y = x / x * abs(y)。
和 ♢，规则如下：
当x小于y时，x ♢ y = y - y - x ⊙ y；
其他情况下，x ♢ y = abs(x) - y - y - 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 / (y / 3 ♢ x)。
运算优先级：♢ > ** = ⊕ > * = / = % > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ♢ 1 ⊙ 9 ⊕ ... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♢ 1 ⊙ 9 ⊕ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 △，规则如下：
当x是偶数时，x △ y = x * y / y；
其他情况下，x △ y = x * y * x。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 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 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = y * y * y * x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - x * x - 3.
and ♢, the rules are as follows:
when x is odd, x ♢ y = 1 - x - 3 ⊙ y;
otherwise, x ♢ y = y + 2 * y ⊙ x.
The precedence of operations: ♢ > ** = ⊗... | {
"game_data": {
"answer": "-1125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♢ 2 ⊙ 10 ⊗ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ♢, the rules are as follows:
when x is greater than y, x ♢ y = 4 / (y) + x * x;
otherwise, x ♢ y = (x * y) + y - x.
and □, the rules are as follows:
when y is odd, x □ y = 4 / y ** (1) ** x;
otherwise, x □ y = y * x.
and ◇, the rules are as follows:
when x is less than y, x ◇ y = x + y - y * 4;
otherwi... | {
"game_data": {
"answer": "0.210526",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 2 ♢ 7",
"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。
和 ☆，规则如下：
当y是奇数时，x ☆ y = x - 1 + y / (x)；
其他情况下，x ☆ y = x * x ♢ y - x。
和 △，规则如下：
当x小于y时，x △ y = y - x + x + 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: 1 △ 4 ☆ 9 ♢ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6.222222",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 4 ☆ 9 ♢ 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 = x + 3 - y + x。
运算优先级：** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 - 10 + 8 ◇ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 - 10 + 8 ◇ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = abs(y + x).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = (2 - y * x).
The precedence of operations: ⊗ > ** = ☆ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculat... | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊗ 7 ☆ 2",
"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 = y - x - y;
otherwise, x ○ y = abs(x) / y.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4 ○ 9
Pl... | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ⊕，规则如下：
当x和y都是奇数时，x ⊕ y = y + x；
其他情况下，x ⊕ y = y + abs(x - x)。
和 ◎，规则如下：
当x和y的和是奇数时，x ◎ y = x / y + y；
其他情况下，x ◎ y = y * y - x。
和 ☆，规则如下：
当y是3的倍数时，x ☆ y = x + y * 3；
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 ☆ 7 ⊕ 10 ◎ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 7 ⊕ 10 ◎ 1",
"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 odd, x ♡ y = (y - 1 + x);
otherwise, x ♡ y = y + x.
and △, the rules are as follows:
when x is greater than y, x △ y = x * y ** x;
otherwise, x △ y = x - x - y.
and ◎, the rules are as follows:
when x is greater than y, x ◎ y = x * y ♡ x;
otherwise, x ◎ y = y + ... | {
"game_data": {
"answer": "899",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 2 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = (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 * x.
The precedence of operations: ** > * = / = % = ♢ > + = - = ◎。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "120.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ** 4 ♢ 4 ◎ 1 ♢ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x + y。
和 ○，规则如下：
实数域上，x ○ y = x ⊕ y。
和 ☆，规则如下：
实数域上，x ☆ y = y - x + x。
运算优先级：☆ > ** = ○ > * = / = % > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ○ 10 ⊕ 4 ○ 7 ☆ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "29",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 10 ⊕ 4 ○ 7 ☆ 7",
"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 = y * x * y。
和 ○，规则如下：
当x大于y时，x ○ y = x + y + y + x；
其他情况下，x ○ y = x ☆ y * x。
运算优先级：** = ☆ = ○ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ○ 8 - 2 ☆ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "56",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 8 - 2 ☆ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ◎, the rules are as follows:
when x is even, x ◎ y = abs(y - y) ** y + x;
otherwise, x ◎ y = x + x + y ** x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y * x * 5 / x.
The precedence of operations: ◎ > ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the express... | {
"game_data": {
"answer": "99",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 1 ** 2 + 10 ▽ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x * y * y + x.
and ▽, 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... | {
"game_data": {
"answer": "648",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ○，规则如下：
当x小于y时，x ○ y = x * y - x + x * 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: 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 □，规则如下：
当x是3的倍数时，x □ y = x * y * y - y；
其他情况下，x □ y = x + y * x。
和 ♡，规则如下：
实数域上，x ♡ y = 4 / y □ x / 2。
运算优先级：♡ > ** > * = / = % = □ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 □ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "70",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 △，规则如下：
当y是3的倍数时，x △ y = y + y * x；
其他情况下，x △ y = abs(x * y / x)。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 * 6 △ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "40",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 * 6 △ 4",
"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 = x - x + 4 + y。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 △ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 7",
"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 + y - x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x + x * 3 + y.
The precedence of operations: ** = ☆ > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calcula... | {
"game_data": {
"answer": "40",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ** 7 ☆ 8 ◇ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = y - y * y / x。
运算优先级：** > * = / = % = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 / 7 ◎ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 / 7 ◎ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ◇，规则如下：
当x是偶数时，x ◇ y = x - y - x；
其他情况下，x ◇ y = 3 * x - y。
运算优先级：** > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ◇ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-8",
"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 = y + 2 ** abs(x - 5 / y)。
和 △，规则如下：
实数域上，x △ y = x - x + y - 4 + y。
运算优先级：△ > ** > * = / = % > + = - = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 6",
"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是奇数时，x ⊙ y = y * y / x / x + y；
其他情况下，x ⊙ y = x + 1 - x + x / y。
和 ⊕，规则如下：
实数域上，x ⊕ y = y / y + x / 4 * 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: 5 % 10 ⊕ 8 ⊙ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 % 10 ⊕ 8 ⊙ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.