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 odd, x ⊕ y = y + (x + x);
otherwise, x ⊕ y = y / x.
and ◎, the rules are as follows:
when y is even, x ◎ y = x + y - 3;
otherwise, x ◎ y = x - x + y.
and ○, the rules are as follows:
when y is a multiple of 3, x ○ y = x + y - 4;
otherwise, x ○ y =... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊕ 7 ○ 9 ◎ 9 + 3",
"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 less than y, x △ y = x - x - y - 1;
otherwise, x △ y = y - y + x * x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expres... | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 7 △ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = 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 ▽ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "24",
"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都是奇数时，x □ y = y - 3 * x；
其他情况下，x □ y = x + y + x。
和 ♢，规则如下：
实数域上，x ♢ y = x □ y - 5 * 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: 10 / 10 □ 1 ♢ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.138889",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 / 10 □ 1 ♢ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ⊕，规则如下：
当x和y的和是奇数时，x ⊕ y = y + y + y - x - x；
其他情况下，x ⊕ y = x + y。
和 ☆，规则如下：
实数域上，x ☆ y = x ⊕ x + y * y - 4。
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: 3 ☆ 5 / 6 - 3 ⊕ 6 □ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-13.444444",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 5 / 6 - 3 ⊕ 6 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = 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 ▽ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "30",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 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和y都是奇数时，x ⊗ y = y + x / 3；
其他情况下，x ⊗ y = x - x + y。
和 ◎，规则如下：
当x是5的倍数时，x ◎ y = x - x - y；
其他情况下，x ◎ y = x + y ⊗ x。
和 ⊕，规则如下：
当x和y都是偶数时，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: 10 ⊕ 8 ◎ 9 ⊗ 6 ** 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊕ 8 ◎ 9 ⊗ 6 ** 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y + x。
和 ▽，规则如下：
当y是3的倍数时，x ▽ y = abs(y - y * x)；
其他情况下，x ▽ y = abs(y ** x)。
运算优先级：□ = ▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ▽ 8 □ 4 - 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "506",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 8 □ 4 - 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ⊙, the rules are as follows:
when y is a multiple of 3, x ⊙ y = x + x + y / x - y;
otherwise, x ⊙ y = x / x + x / x / y.
and ◎, the rules are as follows:
when x is a multiple of 3, x ◎ y = y + (x + y) - y + x;
otherwise, x ◎ y = x / 2 ⊙ x - x * y.
and □, the rules are as follows:
when y is a multiple of ... | {
"game_data": {
"answer": "-8.341667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 1 □ 2 ◎ 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 = 1 / y + abs(x).
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 cal... | {
"game_data": {
"answer": "-96822.319964",
"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,
"... |
logic-v2 | Define ○, the rules are as follows:
when y is even, x ○ y = y / abs(5 - y - x * y);
otherwise, x ○ y = 4 + 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 expr... | {
"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) + 3 + x.
and ◎, the rules are as follows:
when y is odd, x ◎ y = y * x;
otherwise, x ◎ y = y * abs(x - y).
and ♡, the rules are as follows:
when the sum of x and y is even, x ♡ y = y - x - y;
otherwise, x ♡ y = y + x.
The precedence of ... | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 1 ♡ 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。
和 ◎，规则如下：
当y是偶数时，x ◎ y = y + y / x；
其他情况下，x ◎ y = y - (x - x)。
运算优先级：** > * = / = % = ◎ > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ♡ 8 ◎ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 8 ◎ 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 * 3 * 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 ◇ 5 % 5
Please fill y... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 5 % 5",
"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和y都是奇数时，x ▽ y = y + (y) + 5 * 5 + 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: 2 ▽ 7 ▽ 10 * 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "48",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 7 ▽ 10 * 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = y + x * 5 + x - 3。
运算优先级：** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 + 5 △ 3 / 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "46.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 + 5 △ 3 / 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = x + x * y.
and ◇, the rules are as follows:
when the sum of x and y is even, x ◇ y = x - x - y;
otherwise, x ◇ y = x * y - y.
The precedence of operations: ** = ◇ > * = / = % = ♡ > + = -。
Parentheses have the highest priority, and the expressio... | {
"game_data": {
"answer": "-50",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 10 ♡ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = (x - y + y * x * y)。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6
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:
when y is a multiple of 3, x ▽ y = x - y + x - y / y;
otherwise, x ▽ y = y + x - 5 / abs(x) * y.
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the va... | {
"game_data": {
"answer": "17.833333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 + 2 ▽ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = 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: 2 ▽ 9 + 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "83",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 9 + 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = x + (y * y)。
和 △，规则如下：
实数域上，x △ y = y - y - x。
运算优先级：◎ > ** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ◎ 3 △ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 3 △ 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 = x - y + x / y - x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y - y ** x + 2 ⊕ x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x - y + y ▽ x + x.
The precedence of operations: ⊕ > ♡ > ** > * = / = %... | {
"game_data": {
"answer": "108.621903",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 9 ♡ 2 ▽ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define □, the rules are as follows:
when the sum of x and y is even, x □ y = (y / x) + x;
otherwise, x □ y = (x * y).
and ♡, the rules are as follows:
on the real number field, x ♡ y = (y) + 3 + x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y - x - x.
The precedence of operations: ** > *... | {
"game_data": {
"answer": "-702",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 1 □ 6 □ 7 ♡ 9",
"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。
和 ♡，规则如下：
当x和y的和是偶数时，x ♡ y = y ♢ x；
其他情况下，x ♡ y = x * 1 * y。
和 ▽，规则如下：
实数域上，x ▽ y = x + y - y。
运算优先级：♢ = ▽ > ** > * = / = % > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ♢ 3 ▽ 5 ♡ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 3 ▽ 5 ♡ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = x - y + 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 ▽ 2 + 6 % 5
Please fill your ... | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 2 + 6 % 5",
"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 = 2 * x ** y。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = x - x - y。
和 ◇，规则如下：
实数域上，x ◇ y = y - y ⊙ x。
和 ◎，规则如下：
当x和y的和是奇数时，x ◎ y = y ◇ x * y；
其他情况下，x ◎ y = x * y - x。
运算优先级：⊙ = ◎ > ** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ◎ 1 ◇ 9 ⊙ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 1 ◇ 9 ⊙ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ○, the rules are as follows:
when x is a multiple of 3, 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... | {
"game_data": {
"answer": "29",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 - 10 - 5 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y * y - x - y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = abs(y * y) + x + y.
and □, the rules are as follows:
on the real number field, x □ y = y * x * y.
The precedence of operations: □ > ** > * = / = % > + = - = △ = ⊕... | {
"game_data": {
"answer": "-133",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 5 △ 9 ⊕ 4",
"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。
和 ▽，规则如下：
实数域上，x ▽ y = x + y - y。
和 ⊗，规则如下：
当x是3的倍数时，x ⊗ y = x - y * 5；
其他情况下，x ⊗ y = y ⊕ 1 ** x。
运算优先级：** > * = / = % > + = - = ⊕ = ▽ = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ▽ 7 ⊗ 8 ⊕ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 7 ⊗ 8 ⊕ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = 2 - (x * y) * y。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - abs(x + x * x / x).
and ○, the rules are as follows:
when y is even, x ○ y = x - y ** x / y;
otherwise, x ○ y = (y) + x - x ⊙ x - y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x ○ x + y.
The precedence of operation... | {
"game_data": {
"answer": "40",
"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_dep... |
logic-v2 | Define ◇, the rules are as follows:
when x and y are both odd, x ◇ y = y * y * x + y;
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 the ... | {
"game_data": {
"answer": "0.003906",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 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是奇数时，x ⊗ y = x + y - 4；
其他情况下，x ⊗ y = (y - x / x)。
和 ☆，规则如下：
实数域上，x ☆ y = y - (x) ⊗ y。
和 ♡，规则如下：
当y是3的倍数时，x ♡ y = x * y * x；
其他情况下，x ♡ y = y + x + x。
运算优先级：♡ > ** = ⊗ = ☆ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊗ 8 ☆ 10 ♡ 9
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 ☆ 10 ♡ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = (x ** y * x)。
和 ⊙，规则如下：
实数域上，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: 9 ⊙ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.035156",
"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_d... |
logic-v2 | Define ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = y - abs(y) - 1 - x;
otherwise, x ♡ y = y ** x + x.
and ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = x ♡ x + y;
otherwise, x ⊙ y = x * y.
The precedence of operations: ⊙ > ** > * = / = % = ♡ > + = -。
Parentheses h... | {
"game_data": {
"answer": "-11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 5 ♡ 10 ♡ 1 ⊙ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y + abs(y + x) + x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x + x - 1 ♡ y.
The precedence of operations: ♡ > ** > * = / = % > + = - = ♢。
Parentheses have the highest priority, and the expression inside the parentheses i... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 1",
"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 = 5 * y + 4 - x；
其他情况下，x □ y = 4 + y - y - x。
和 ⊗，规则如下：
当y是偶数时，x ⊗ y = y * x - 4；
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: 9 ⊗ 6 □ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-31",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 6 □ 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 * x / 3.
and ⊕, the rules are as follows:
when x is even, x ⊕ y = y ** x ⊗ x;
otherwise, x ⊕ y = (x - y) ⊗ x.
and ◇, the rules are as follows:
when x is odd, x ◇ y = abs(x + y);
otherwise, x ◇ y = x + 2 + y.
The precedence of operations: ... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 8 ◇ 3 ⊗ 3 - 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
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 - 3 + x - x ⊗ y。
和 ⊕，规则如下：
实数域上，x ⊕ y = x * 1 + 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 ⊕ 10 ◇ 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 ⊕ 10 ◇ 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:
on the real number field, x ○ y = x + y / x + y.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ○ 8 / 6
Please fill your ... | {
"game_data": {
"answer": "2.690476",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 8 / 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ◎, the rules are as follows:
when x is odd, x ◎ y = y + y + x - y + y;
otherwise, x ◎ y = x * x * 4 * x + y.
and △, the rules are as follows:
on the real number field, x △ y = y / x + x * y.
The precedence of operations: ◎ > ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the express... | {
"game_data": {
"answer": "170.588235",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 6 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = y / y + (x) + x + x.
The precedence of operations: ** > * = / = % > + = - = ▽。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 + 3 + 10 ▽ 5
Please... | {
"game_data": {
"answer": "49",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 + 3 + 10 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 △，规则如下：
当y是偶数时，x △ y = y + y + x；
其他情况下，x △ y = 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 △ 2 ** 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 2 ** 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ☆, the rules are as follows:
when x is odd, x ☆ y = x * x + y;
otherwise, 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 par... | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ☆, the rules are as follows:
when x is odd, x ☆ y = y / (x + y);
otherwise, 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 parenth... | {
"game_data": {
"answer": "251",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊙ 3 ⊙ 5 ☆ 8 ☆ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | 定义 ☆，规则如下：
当x大于y时，x ☆ y = x - x * y；
其他情况下，x ☆ y = x + y + x * y。
和 □，规则如下：
当x是偶数时，x □ y = y - x + x + x；
其他情况下，x □ y = 3 / y - x / x + y。
运算优先级：□ > ** > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ☆ 1 ☆ 4 □ 10 + 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 1 ☆ 4 □ 10 + 5",
"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 and y are both even, x ◇ y = x * y / x;
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 expressio... | {
"game_data": {
"answer": "-11.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 2 / 4",
"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 even, x △ y = y * x / x * x + x;
otherwise, x △ y = 1 - x + (3) - x ** y.
The precedence of operations: ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the ex... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 1 + 7",
"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y是3的倍数时，x ⊗ y = x + y + x - x * y；
其他情况下，x ⊗ y = x + 1 * (x - y)。
和 △，规则如下：
实数域上，x △ y = x + 3 * y ⊗ 5 * 5。
和 ◎，规则如下：
实数域上，x ◎ y = 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: 2 ◎ 1 △ 3 ⊗ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-15879",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 1 △ 3 ⊗ 5",
"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 + 2 + 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
Please fill your final an... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ⊗，规则如下：
当x小于y时，x ⊗ y = abs(x * y - y - 2)；
其他情况下，x ⊗ y = y / x - y / y - x。
和 ⊙，规则如下：
实数域上，x ⊙ y = x * y ⊗ x + 3 + 5。
和 ♢，规则如下：
实数域上，x ♢ 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: 3 ♢ 3 ⊙ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-28.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 3 ⊙ 3",
"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 = abs(y * y - x)。
和 ◎，规则如下：
实数域上，x ◎ y = x + (x ☆ y)。
和 ⊙，规则如下：
当x是5的倍数时，x ⊙ y = y ◎ x + x；
其他情况下，x ⊙ y = 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: 5 ☆ 2 ⊙ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3964",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ☆ 2 ⊙ 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:
when y is even, x ◎ y = 2 - y / y + x;
otherwise, x ◎ y = y + x - (x - x).
and □, the rules are as follows:
when x is a multiple of 5, x □ y = x + y * y + abs(x);
otherwise, x □ y = x - y * x ◎ 5.
The precedence of operations: □ > ** > * = / = % > + = - = ◎。
Parentheses have ... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 □ 5 ◎ 9",
"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.
and △, the rules are as follows:
when x is a multiple of 3, x △ y = x ⊗ x * y / x;
otherwise, x △ y = abs(4) + y + x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = 4 * x - y ⊗ 2 * x.
The precedence of operations: ♡... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 1 ♡ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x - 5 + y - y。
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: 5 ♡ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 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 + (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... | {
"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 | Define △, the rules are as follows:
when y is odd, x △ y = x * 1 * y;
otherwise, x △ y = 4 / x + abs(y).
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3 △ 1... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 □，规则如下：
当x小于y时，x □ y = (y * y - x)；
其他情况下，x □ y = y * y - x * x。
和 ◎，规则如下：
当y是5的倍数时，x ◎ y = x * abs(y + y) + y - y；
其他情况下，x ◎ y = y ** x + 5 * y * y。
运算优先级：** > * = / = % = □ > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◎ 6 ◎ 8 □ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 6 ◎ 8 □ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ▽, the rules are as follows:
when x is less than y, x ▽ y = y + x + 5;
otherwise, x ▽ y = x - 3 + x + y.
The precedence of operations: ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = x + abs(x * 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 - 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: 10 ⊕ 7 ♢ 5 ⊙ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "55842",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊕ 7 ♢ 5 ⊙ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ⊗, the rules are as follows:
when y is a multiple of 5, x ⊗ y = x - y + y / 5 - 5;
otherwise, x ⊗ y = x * x + x - y - (x).
and ♢, the rules are as follows:
when x and y are both odd, x ♢ y = x ⊗ y;
otherwise, x ♢ y = (x + x + y).
and ☆, the rules are as follows:
on the real number field, x ☆ y = x * y ... | {
"game_data": {
"answer": "26889",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 7 ☆ 6 ⊗ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x * (y * y + x + y).
and ▽, the rules are as follows:
when x is greater than y, x ▽ y = 3 ** y + x ◎ y;
otherwise, x ▽ y = x - y - y * y / y.
The precedence of operations: ** = ◎ > * = / = % > + = - = ▽。
Parentheses have the highest priority, a... | {
"game_data": {
"answer": "189",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = 2 + x ** (x * y).
and △, the rules are as follows:
on the real number field, x △ y = x ♡ x / y * 1.
The precedence of operations: ♡ > ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses is ... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 6 ♡ 7 + 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ◎, the rules are as follows:
when y is odd, x ◎ y = x / y - x ** 4;
otherwise, x ◎ y = x ** (x) - y.
and □, the rules are as follows:
on the real number field, x □ y = abs(x / y).
The precedence of operations: □ > ** = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside ... | {
"game_data": {
"answer": "3121",
"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 | 定义 ▽，规则如下：
当x和y都是偶数时，x ▽ y = y + y * x - 2 + 2；
其他情况下，x ▽ y = x - y / 4 - 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: 9 - 10 * 5 ▽ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-49.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 - 10 * 5 ▽ 3",
"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 + y - x。
和 ▽，规则如下：
实数域上，x ▽ y = y ♢ x - x。
和 ○，规则如下：
实数域上，x ○ y = y + x + 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 ▽ 10 ♢ 8 * 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "79",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 5 ▽ 10 ♢ 8 * 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define ♢, the rules are as follows:
when x is greater than y, x ♢ y = x + (y) * x - x;
otherwise, x ♢ y = x + y + x - 2.
and ◇, the rules are as follows:
when y is even, x ◇ y = x * y * y - y;
otherwise, x ◇ y = x ♢ y - y + x.
and ◎, the rules are as follows:
when x and y are both odd, x ◎ y = (y - x) / x - x... | {
"game_data": {
"answer": "57",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 1 ◎ 4 ◇ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = (x + y)。
运算优先级：◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x + (y).
and ♡, the rules are as follows:
on the real number field, x ♡ y = y - (x - x) ☆ x * x.
The precedence of operations: ** > * = / = % > + = - = ☆ = ♡。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"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 + 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 ▽ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 △，规则如下：
当x是5的倍数时，x △ y = y * x + y * 5；
其他情况下，x △ y = y - x - 4 / x + x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = 2 ** abs(x + y - y).
and ◇, the rules are as follows:
on the real number field, x ◇ y = y + abs(x - x).
and ▽, the rules are as follows:
on the real number field, x ▽ y = y - y / x ** 1.
The precedence of operations: ◇ = ▽ > ** = ⊗ > * = / = % ... | {
"game_data": {
"answer": "1024",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊗ 1 ▽ 1 ◇ 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 = 2 - y - x * y。
和 ▽，规则如下：
实数域上，x ▽ y = x * y * x □ 2。
运算优先级：□ = ▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 □ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ◎，规则如下：
当x和y都是奇数时，x ◎ y = x / y；
其他情况下，x ◎ y = x + (y - y)。
和 ▽，规则如下：
当y是偶数时，x ▽ y = 3 + y + x；
其他情况下，x ▽ y = y * x ◎ x。
运算优先级：** > * = / = % > + = - = ◎ = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 * 4 ▽ 2 ◎ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 * 4 ▽ 2 ◎ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = x + y - x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 △ 4 % 6 ** 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 4 % 6 ** 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 △，规则如下：
当x等于y时，x △ y = 1 + y * x + x；
其他情况下，x △ y = 3 + 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: 3 △ 8 * 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "128",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 8 * 8",
"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 = x / y / y.
and ◎, the rules are as follows:
when x is a multiple of 3, x ◎ y = 3 - 4 ♡ x / y;
otherwise, x ◎ y = x + y * x - y.
The precedence of operations: ** = ◎ > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the express... | {
"game_data": {
"answer": "-0.0118",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 4 - 8 ♡ 4 ◎ 7",
"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 = y - abs(y) - x * y;
otherwise, 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 the expression: 8 ▽... | {
"game_data": {
"answer": "-40",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ▽，规则如下：
当x和y都是奇数时，x ▽ y = abs(y - x ** y - x)；
其他情况下，x ▽ y = x + y。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 + 3 ▽ 4
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 ▽ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ◇，规则如下：
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: 2 ◇ 7 ◇ 1 * 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 ◇ 7 ◇ 1 * 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 + y - 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 ○ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ⊗, the rules are as follows:
when x and y are both even, x ⊗ y = x * y - y;
otherwise, x ⊗ y = y / x / x.
and ◎, the rules are as follows:
when y is odd, x ◎ y = 2 ⊗ y * x;
otherwise, x ◎ y = (x - 1) + y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x * 1 / y.
The precedence of op... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 2 ▽ 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:
on the real number field, x ⊙ y = x * (x - y * y).
and ◇, the rules are as follows:
on the real number field, x ◇ y = x + x ** x ⊙ y.
and ○, the rules are as follows:
on the real number field, x ○ y = x - 2 / y * 3.
The precedence of operations: ◇ > ⊙ = ○ > ** > * = / = % > + =... | {
"game_data": {
"answer": "-150.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊙ 5 ○ 10",
"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 + y + x * x。
和 ◇，规则如下：
当x和y的和是偶数时，x ◇ y = abs(y + y / x * y) ** x；
其他情况下，x ◇ y = y + x。
运算优先级：** = ♡ > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 / 6 ◇ 10 ♡ 7 ♡ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "13814.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 / 6 ◇ 10 ♡ 7 ♡ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,... |
logic-v2 | Define ○, the rules are as follows:
when x and y are both odd, x ○ y = x - y - x;
otherwise, x ○ y = y * y - x.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression... | {
"game_data": {
"answer": "95",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = 5 + x * y * x * 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
Please fill your fina... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = (x ** y) + 5 + x ** 4。
和 ○，规则如下：
实数域上，x ○ y = x * y + 5。
和 △，规则如下：
实数域上，x △ y = 4 * x - y ** x + x。
运算优先级：⊕ > △ > ** > * = / = % = ○ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊕ 3 △ 4 ○ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-16344",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 3 △ 4 ○ 1",
"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 = (x) + y * x.
and ⊕, the rules are as follows:
when x is greater than y, x ⊕ y = x - y * x;
otherwise, x ⊕ y = y * y + x - y.
The precedence of operations: ○ = ⊕ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression... | {
"game_data": {
"answer": "-168",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 6 ⊕ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y + 5 * 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: 9 △ 7
Please fill your final an... | {
"game_data": {
"answer": "52",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 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 = x * abs(y) + x。
和 △，规则如下：
实数域上，x △ y = y / x / y。
和 ♡，规则如下：
实数域上，x ♡ y = abs(y) + x / y。
运算优先级：⊙ = △ > ** > * = / = % > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ♡ 3 ⊙ 6 △ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "105.047619",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 3 ⊙ 6 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ◇, the rules are as follows:
when x is a multiple of 5, x ◇ y = x * 2 + y;
otherwise, x ◇ y = y + y - x.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = x * 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 / 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 ◇ 1 ⊙ 6 △ 8 % 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2351.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◇ 1 ⊙ 6 △ 8 % 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x - x + y。
和 ⊕，规则如下：
当x是5的倍数时，x ⊕ y = x - y - x；
其他情况下，x ⊕ y = x □ 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: 6 □ 1 ⊕ 3 - 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 1 ⊕ 3 - 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y - x * x + y。
运算优先级：⊗ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ⊗ 6 % 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 6 % 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ♡，规则如下：
当x大于y时，x ♡ y = x * 3 + (y * x) * 2；
其他情况下，x ♡ y = x * y。
和 ⊙，规则如下：
当x和y的和是偶数时，x ⊙ y = x * x - y * x * y；
其他情况下，x ⊙ y = abs(y + x * x) / y。
运算优先级：♡ = ⊙ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 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 ♡ 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和y的和是奇数时，x △ y = x - x ** x - y；
其他情况下，x △ y = y + 3 - x - y。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 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 = x * y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x * 4 + 1 + y.
The precedence of operations: ** = ☆ > * = / = % > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "105",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 % 3 ◇ 10 ☆ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define △, the rules are as follows:
when y is a multiple of 3, x △ y = y - x ** y;
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 express... | {
"game_data": {
"answer": "-19673",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 9 △ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y - y / x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = abs(y - 1) - y + x.
The precedence of operations: ⊕ > ** = □ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is ca... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
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