env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y - x * 2 - y.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5
Please fill your final an... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊗, the rules are as follows:
when x is less than y, x ⊗ y = x * x * abs(y);
otherwise, x ⊗ y = y - y + x * x.
and △, the rules are as follows:
on the real number field, x △ y = 4 * x + y * x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = x ⊗ y + x + y.
The precedence of operations: ⊗... | {
"game_data": {
"answer": "324",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 2 ⊗ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x * (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: 1 % 3 △ 8
Please fill you... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 % 3 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = y + y * x。
和 ▽，规则如下：
实数域上，x ▽ y = 2 / x / y + y。
和 ☆，规则如下：
当x等于y时，x ☆ y = 1 ▽ y * x；
其他情况下，x ☆ y = x ▽ y - y - x。
运算优先级：▽ > ☆ > ** > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ▽ 9 ☆ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-8.911385",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 9 ☆ 2",
"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 = y - y - x - x。
和 ▽，规则如下：
实数域上，x ▽ y = y * y - 5 * y + x。
和 □，规则如下：
实数域上，x □ y = x * y △ y - y * 4。
运算优先级：□ > ** = ▽ > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 6 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "72",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 6 △ 8",
"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y是5的倍数时，x □ y = x + y * x；
其他情况下，x □ y = y * x * y。
和 ◇，规则如下：
实数域上，x ◇ y = y - x - x。
运算优先级：□ = ◇ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 □ 8 ◇ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-761",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 8 ◇ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ⊕，规则如下：
当y是奇数时，x ⊕ y = y - y - y - x；
其他情况下，x ⊕ y = y + x - y + y。
和 ♡，规则如下：
当x和y都是偶数时，x ♡ y = y ** x；
其他情况下，x ♡ y = (y + x)。
和 ◇，规则如下：
当y是偶数时，x ◇ y = y + x；
其他情况下，x ◇ y = y - x ⊕ 3 * y。
运算优先级：** = ⊕ = ♡ > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ◇ 6 ⊕ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 6 ⊕ 10",
"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 - x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = 3 - x * y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x / 3 / 1 - y.
The precedence of operations: ** = ⊕ > * = / = % = ☆ = ▽ > + = -。
Par... | {
"game_data": {
"answer": "-205",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 4 ⊕ 10 ▽ 3 + 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x - 4 + y.
and ◎, the rules are as follows:
when y is a multiple of 5, x ◎ y = x ♢ y - y;
otherwise, x ◎ y = y + x - 2.
and ☆, the rules are as follows:
when y is a multiple of 5, x ☆ y = abs(y * x) * x;
otherwise, x ☆ y = x + y - 5.
The pr... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♢ 2 ☆ 8 ◎ 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 + x - y - y - x.
and ⊕, the rules are as follows:
when y is even, x ⊕ y = (4 □ x + 3) * y - y;
otherwise, x ⊕ y = (2 + y * x).
The precedence of operations: □ > ** > * = / = % = ⊕ > + = -。
Parentheses have the highest priority, and the expres... | {
"game_data": {
"answer": "-25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 8 * 9 ⊕ 5 □ 8",
"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 * 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
Please fill your final answer... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ☆, the rules are as follows:
when x and y are both odd, x ☆ y = x - y * y;
otherwise, x ☆ 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 t... | {
"game_data": {
"answer": "6084",
"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_d... |
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: 7 / 10 △ 3 - 9
Please fill your f... | {
"game_data": {
"answer": "-5.3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 / 10 △ 3 - 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = y / x / y + x + y.
and □, the rules are as follows:
on the real number field, x □ y = y - 5 + y / x + 2.
and ○, the rules are as follows:
on the real number field, x ○ y = y + y □ x - y * x.
The precedence of operations: ⊗ > ** = ○ > * = / = % ... | {
"game_data": {
"answer": "7.914284",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 + 2 ⊗ 6 ⊗ 8 ○ 7 □ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y - x / (y - 3 - y).
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x / y / abs(x - x + x).
and ⊙, the rules are as follows:
when x and y are both odd, x ⊙ y = 4 / x + x * x ◎ y;
otherwise, x ⊙ y = 1 - y - x ⊕ x.
The prece... | {
"game_data": {
"answer": "-5.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 3 ⊕ 9 ⊙ 1",
"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.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * y - (x ⊕ 1).
and □, the rules are as follows:
when x is equal to y, x □ y = y + x + y / y;
otherwise, x □ y = y ⊕ y / x.
The precedence of operations: ** > * = ... | {
"game_data": {
"answer": "3916",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 4 ⊕ 10 ⊙ 4",
"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).
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 ○ 3
Please fill your final answ... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 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 = y + y - x / x。
和 ◎，规则如下：
实数域上，x ◎ y = x + y + x * y。
和 ▽，规则如下：
当x是3的倍数时，x ▽ y = x / x * y * y + x；
其他情况下，x ▽ y = 1 * 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: 6 ◎ 5 ⊙ 4 ▽ 4 ⊙ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "41",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 5 ⊙ 4 ▽ 4 ⊙ 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 = (x + 3 - y) - y。
和 □，规则如下：
实数域上，x □ y = y - x - x。
和 ⊗，规则如下：
当y是偶数时，x ⊗ y = x / abs(y ** 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: 2 * 7 ⊗ 10 ○ 5 □ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "18.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 * 7 ⊗ 10 ○ 5 □ 4",
"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 odd, x ⊕ y = x - y - y - x - x;
otherwise, x ⊕ y = x / y * x + x - 1.
and ○, the rules are as follows:
when x is even, x ○ y = y + x ** y ⊕ x;
otherwise, x ○ y = y - x - x * y.
The precedence of operations: ** > * = / = % = ○ > + = - = ⊕。
Parentheses have the highes... | {
"game_data": {
"answer": "-28",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 5 + 5 ○ 1",
"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 = 4 / (x) - y。
和 ◇，规则如下：
实数域上，x ◇ y = x + 5 □ 5 / y。
运算优先级：** = □ > * = / = % = ◇ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 % 1 ◇ 10 □ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 % 1 ◇ 10 □ 2",
"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 = y - x + x + 3。
和 ◎，规则如下：
当x大于y时，x ◎ y = x ** y；
其他情况下，x ◎ y = x * y + 5。
运算优先级：☆ > ** > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ◎ 4 ☆ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "33",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 4 ☆ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = abs(x) - x - y。
和 ☆，规则如下：
实数域上，x ☆ y = y + y * abs(x)。
和 ▽，规则如下：
当y是奇数时，x ▽ y = y - y ☆ x；
其他情况下，x ▽ y = x - x - (y)。
运算优先级：** > * = / = % = ☆ = ▽ > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ▽ 5 ⊕ 9 ☆ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-62",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 5 ⊕ 9 ☆ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ◇，规则如下：
实数域上，x ◇ y = x - y - y - 3 + 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 | 定义 ☆，规则如下：
当x是5的倍数时，x ☆ y = y + 1 * x；
其他情况下，x ☆ y = x + x - y。
和 ◎，规则如下：
当x和y都是奇数时，x ◎ y = abs(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: 8 - 9 ☆ 6 ◎ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 - 9 ☆ 6 ◎ 2",
"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.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4
Please fill your final answer in ... | {
"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 | 定义 △，规则如下：
实数域上，x △ y = x + 3 + 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: 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ▽，规则如下：
当x大于y时，x ▽ y = y / y - y ** x；
其他情况下，x ▽ y = 2 - y / 2 - x + 4。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y + y + x * y。
运算优先级：** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ▽ 3 - 4 - 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "28",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 3 - 4 - 4",
"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 - 3 * y + 3 / 3.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x + y - 5 / 4.
The precedence of operations: ** = □ > * = / = % = ◇ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is... | {
"game_data": {
"answer": "737.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ** 3 ◇ 1 - 5 □ 5",
"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 - abs(y + x) - x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * y + x + y ⊗ x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = y - x + 3 + x ⊗ y.
The precedence of operations: ** = ⊗ > * = / = %... | {
"game_data": {
"answer": "11523",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ♢ 4 ⊙ 10 ⊗ 9",
"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 = 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 ◇ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"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 + 5 * 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 ** 5 ◇ 4
Please fill your... | {
"game_data": {
"answer": "6140",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ** 5 ◇ 4",
"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 - y；
其他情况下，x ○ y = y / x + x。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ○ 8 / 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.944444",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 8 / 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 △，规则如下：
当x小于y时，x △ y = x + y + x；
其他情况下，x △ y = y - y / x。
运算优先级：** = △ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 % 4 △ 10 △ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 % 4 △ 10 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ⊙, the rules are as follows:
when x is even, x ⊙ y = y + x * x;
otherwise, x ⊙ y = x / y.
and ☆, the rules are as follows:
when the sum of x and y is odd, x ☆ y = y + x * y;
otherwise, x ☆ y = x * y - y.
and △, the rules are as follows:
on the real number field, x △ y = x / y / x.
The precedence of ope... | {
"game_data": {
"answer": "288",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 9 ⊙ 2 △ 4",
"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 = x - y + x + y。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 % 1 △ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 % 1 △ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 △，规则如下：
当x大于y时，x △ y = x / y * x；
其他情况下，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: 3 △ 9 △ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "441",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 9 △ 1",
"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 less than y, x ⊕ y = x + 2 * y;
otherwise, x ⊕ y = x - x - y.
and ○, the rules are as follows:
when x is odd, x ○ y = x ⊕ (y);
otherwise, x ○ y = y + x + x.
and □, the rules are as follows:
on the real number field, x □ y = y - 1 + x.
The precedence of operations:... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 2 ⊕ 6 □ 10 + 10",
"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 = 5 - y / x - y。
和 ◇，规则如下：
实数域上，x ◇ y = y + y * x - y ** x。
和 ▽，规则如下：
当x和y都是奇数时，x ▽ y = x + 3 + x + y ⊗ x；
其他情况下，x ▽ y = y - y - 1 * 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 ▽ 8 ⊗ 6 ▽ 5 ◇ 5 - 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 8 ⊗ 6 ▽ 5 ◇ 5 - 9",
"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 - 1 / x - x。
和 ♡，规则如下：
当y是3的倍数时，x ♡ y = 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: 1 □ 2 ♡ 5 ♡ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3.1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 2 ♡ 5 ♡ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 ◎，规则如下：
当x小于y时，x ◎ y = 1 - x + y - 5 / y；
其他情况下，x ◎ y = y * 4 + y - x。
和 ○，规则如下：
当x和y的和是奇数时，x ○ y = x / x + y；
其他情况下，x ○ y = y * x + y * x * x。
运算优先级：◎ > ** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ○ 4 ◎ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "19.714286",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 4 ◎ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 ☆，规则如下：
当x小于y时，x ☆ y = abs(x) - x * y - y * y；
其他情况下，x ☆ y = y ** x。
和 ◇，规则如下：
当x等于y时，x ◇ y = y ☆ x - 3；
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: 6 ◇ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-34",
"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 | 定义 ○，规则如下：
实数域上，x ○ y = x - x + (1 * y)。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 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 the sum of x and y is even, x ♢ y = 4 + y + x / y + x;
otherwise, x ♢ y = x - x / y - x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = 1 * 3 * (x / y).
and ○, the rules are as follows:
when x is a multiple of 5, x ○ y = x + (x) / y;
otherwise, x ○ y ... | {
"game_data": {
"answer": "-1.111111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♢ 9 ◎ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 ▽，规则如下：
当y是偶数时，x ▽ y = y - 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: 2 ▽ 9 % 4 + 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7.222222",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 9 % 4 + 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 is less than y, x △ y = y + x - 2 + 5;
otherwise, x △ y = 1 - 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 expres... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 / 4 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = x + 5 - x + x + y。
和 ○，规则如下：
当x和y都是奇数时，x ○ y = (y * y + x) ** y * x；
其他情况下，x ○ y = y ⊙ (x - y) / x。
和 ⊕，规则如下：
实数域上，x ⊕ y = (x - 2 + 5 * 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 ○ 5 ⊙ 6 ⊕ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "23.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 5 ⊙ 6 ⊕ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 ⊙，规则如下：
当x和y都是偶数时，x ⊙ y = x + y；
其他情况下，x ⊙ y = x * y。
和 □，规则如下：
当y是奇数时，x □ y = y * y - x；
其他情况下，x □ y = y - abs(x - y)。
和 ♢，规则如下：
当x是偶数时，x ♢ y = x * x + y；
其他情况下，x ♢ y = y - y + x。
运算优先级：⊙ = ♢ > ** = □ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ⊙ 3 ♢ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊙ 3 ♢ 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等于y时，x ♢ y = y * y + y ** x + 3；
其他情况下，x ♢ y = y * x * 4。
和 ⊗，规则如下：
实数域上，x ⊗ y = x - x - y。
和 ♡，规则如下：
实数域上，x ♡ y = 2 - y + (x) * y * y。
运算优先级：♢ > ** > * = / = % = ⊗ = ♡ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ⊗ 6 ♡ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-98",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 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：
当x是偶数时，x ♡ y = x + y - y；
其他情况下，x ♡ y = y * x + (2)。
和 ☆，规则如下：
实数域上，x ☆ y = 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: 4 ☆ 9 - 9 ♡ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-70",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 9 - 9 ♡ 10",
"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 = y * y * x + y.
and □, 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 cal... | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ▽, the rules are as follows:
when the sum of x and y is odd, x ▽ y = y * y * x;
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 expressio... | {
"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 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x + abs(x) / y。
和 ○，规则如下：
实数域上，x ○ y = 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: 2 ⊗ 5 ♡ 9 ○ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-3.36",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 5 ♡ 9 ○ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ☆, the rules are as follows:
when x and y are both even, x ☆ y = y ** y * x - y;
otherwise, x ☆ y = x * y - (x - y).
and ♡, the rules are as follows:
on the real number field, x ♡ y = x - y - 4 ☆ y.
The precedence of operations: ♡ > ** > * = / = % = ☆ > + = -。
Parentheses have the highest priority, and the... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
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都是偶数时，x △ y = 1 + y * x；
其他情况下，x △ y = x ⊗ x - y。
和 ♢，规则如下：
实数域上，x ♢ y = x △ y + y。
运算优先级：△ > ⊗ > ** > * = / = % = ♢ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♢ 8 ⊗ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♢ 8 ⊗ 9",
"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 = y + (4 * 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: 7
Please fill your fi... | {
"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y是5的倍数时，x ◎ y = y - x + x；
其他情况下，x ◎ y = x + 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: 8 △ 10 ◎ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 10 ◎ 5",
"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 - x / y。
和 ○，规则如下：
实数域上，x ○ y = 2 + 5 + 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 ○ 8 % 2 - 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-5.084507",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 1 ○ 8 % 2 - 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ⊗, the rules are as follows:
when the sum of x and y is even, x ⊗ y = y + y + x;
otherwise, x ⊗ y = y * x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y + x + y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y + x - x.
The precedence of operations: ▽ > ⊗ > ** =... | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 1 ⊗ 1 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y + x / y。
和 △，规则如下：
实数域上，x △ y = x - y ⊙ y + x。
和 ☆，规则如下：
实数域上，x ☆ y = (y) + x。
运算优先级：△ > ** = ☆ > * = / = % > + = - = ⊙。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 △ 1 ⊙ 8 ☆ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "17.823529",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 1 ⊙ 8 ☆ 9",
"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 equal to y, x ⊕ y = x * y + 3 * x * x;
otherwise, x ⊕ y = x / x - x - x ** y.
and ◎, the rules are as follows:
when x is equal to y, x ◎ y = y * y + x ⊕ x;
otherwise, x ◎ y = y / (y + x + 3).
and ◇, the rules are as follows:
on the real number field, x ◇ y = y ** ... | {
"game_data": {
"answer": "-14.509246",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 4 ◎ 6 ◇ 1",
"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 + 3 - 3.
and ○, the rules are as follows:
when x is less than y, x ○ y = y + y □ x - x;
otherwise, x ○ y = x * x □ y ** y.
The precedence of operations: ○ > ** > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expres... | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ○ 9 □ 1",
"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3的倍数时，x ☆ y = x + x + y；
其他情况下，x ☆ y = y / y + x * y。
和 ○，规则如下：
实数域上，x ○ y = x / (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: 6 ○ 1 - 7 ☆ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-56.625",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 1 - 7 ☆ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x + y - x.
and ◇, the rules are as follows:
when y is even, x ◇ y = y - x - y;
otherwise, x ◇ y = x * y ** y.
The precedence of operations: ◇ > ** > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expression inside the par... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 1 + 9 ☆ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 △，规则如下：
当x和y的和是奇数时，x △ y = x * x + 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: 10 △ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 △，规则如下：
当y是5的倍数时，x △ y = abs(x + y)；
其他情况下，x △ y = y * x - x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 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:
when x is a multiple of 5, x ▽ y = abs(y) - y + x + x;
otherwise, x ▽ y = x + x - y.
The precedence of operations: ** > * = / = % = ▽ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the e... | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 7 ** 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ⊗，规则如下：
当x是偶数时，x ⊗ y = x + abs(y)；
其他情况下，x ⊗ y = x + x * y。
和 □，规则如下：
当x大于y时，x □ y = x ⊗ y；
其他情况下，x □ y = (x) + y。
和 ○，规则如下：
当y是5的倍数时，x ○ y = y □ 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: 8 □ 7 ○ 10 ⊗ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1380",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 □ 7 ○ 10 ⊗ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = (y + x * 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。
和 ⊕，规则如下：
当x是偶数时，x ⊕ y = y ** 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: 3 ⊕ 3 ♢ 10 ☆ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "60",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊕ 3 ♢ 10 ☆ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | 定义 □，规则如下：
当x是偶数时，x □ y = y / y + x；
其他情况下，x □ y = (y * x) * y。
和 △，规则如下：
实数域上，x △ y = y + x * x。
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 △ 6 △ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3034",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 7 △ 6 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ⊙，规则如下：
当x小于y时，x ⊙ y = x * y + x - 3；
其他情况下，x ⊙ y = (y + x)。
和 ♡，规则如下：
实数域上，x ♡ y = y * x - y ⊙ y。
和 ⊗，规则如下：
当y是3的倍数时，x ⊗ y = x * y ⊙ y；
其他情况下，x ⊗ y = y / 1 ** 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 ⊗ 4 ♡ 8 ⊙ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "29",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 4 ♡ 8 ⊙ 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 = (y ** 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 = x * y。
和 ⊕，规则如下：
实数域上，x ⊕ y = y / y / x。
运算优先级：⊙ = ◎ > ** > * = / = % = ⊕ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ◎ 3 ⊙ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 3 ⊙ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = x * x - y。
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 = x - 3 ⊙ 3 + y。
运算优先级：** = ☆ = ⊙ > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 △ 3 ⊙ 4 ☆ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 3 ⊙ 4 ☆ 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.
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 parentheses is calculated firs... | {
"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:
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 calculated first.
Please calculate the value of the expression: 6 + 9 ▽ 9 ▽ 7
Please fill your ... | {
"game_data": {
"answer": "11.444444",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 + 9 ▽ 9 ▽ 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 and y are both odd, x ⊕ y = y - x * y;
otherwise, x ⊕ y = x + y.
and ◎, the rules are as follows:
when x is greater than y, x ◎ y = x + x ⊕ y;
otherwise, x ◎ y = y ⊕ x.
and ☆, the rules are as follows:
when x is a multiple of 5, x ☆ y = 3 * (y ◎ x);
otherwise, x ☆ y ... | {
"game_data": {
"answer": "75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ☆ 7 ⊕ 10 ◎ 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 x is even, x △ y = y + x * x;
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: 8
Please ... | {
"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 = 1 + y + x.
and ♢, the rules are as follows:
when x is even, x ♢ y = (x + x) ☆ y / x;
otherwise, x ♢ y = y + y + (x - y).
The precedence of operations: ☆ > ♢ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression ins... | {
"game_data": {
"answer": "19",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ▽，规则如下：
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: 4 % 1 - 7 ▽ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 % 1 - 7 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ◎, the rules are as follows:
when x is greater than y, x ◎ y = (x * y * y) * x ** x;
otherwise, x ◎ y = (y + x) + 1.
and △, the rules are as follows:
when x and y are both odd, x △ y = x + x - y ◎ y / y;
otherwise, x △ y = 2 - x * 2 * y ◎ y.
The precedence of operations: △ > ** = ◎ > * = / = % > + = -。
P... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◎ 6",
"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 and y are both odd, x □ y = x - y - y - 2;
otherwise, x □ y = y + x / y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = 2 + (4 □ y) ** x.
The precedence of operations: □ > ** = ⊙ > * = / = % > + = -。
Parentheses have the highest priority, and the expr... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 □ 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:
when y is a multiple of 5, x ▽ y = 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 expression: 8... | {
"game_data": {
"answer": "0.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 7 ▽ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define ♢, the rules are as follows:
when x is even, x ♢ y = abs(y + y - x);
otherwise, x ♢ y = y + y + x.
and △, the rules are as follows:
when y is a multiple of 3, x △ y = y ♢ (y + x);
otherwise, x △ y = y - x + y.
and ⊗, the rules are as follows:
when x is greater than y, x ⊗ y = x * y - y;
otherwise, x ⊗ ... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 - 10 ⊗ 3 △ 6 ♢ 9",
"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 = 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: 3 + 5 ○ 1 ○ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "138",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 + 5 ○ 1 ○ 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 = y - y - x.
and △, 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 t... | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◎ 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 = x - x + x * y；
其他情况下，x ☆ y = y + x * y + abs(1 - x)。
和 □，规则如下：
实数域上，x □ y = 3 / x ☆ y * 1。
运算优先级：** > * = / = % > + = - = ☆ = □。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ☆ 10 □ 9 - 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7.247423",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 10 □ 9 - 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = y + 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 ○ 7
Please fill your final answer... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x * 3 - y.
and ♡, the rules are as follows:
when x is equal to y, x ♡ y = y ◎ (y - y * x);
otherwise, x ♡ y = y - x ◎ x + 4.
The precedence of operations: ◎ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the expression... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": ... |
logic-v2 | 定义 △，规则如下：
实数域上，x △ y = x - y + y。
运算优先级：** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 △ 3 * 4 ** 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 3 * 4 ** 2",
"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 = 1 - y - 5 / 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: 1 △ 9 ** 2 * 3
Please f... | {
"game_data": {
"answer": "-12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 9 ** 2 * 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y * x * y * 2.
and □, the rules are as follows:
on the real number field, x □ y = 5 * y + x.
The precedence of operations: △ > ** > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calcula... | {
"game_data": {
"answer": "66",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 2 □ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ♡，规则如下：
当y是偶数时，x ♡ y = y + x + (x) + 4 + y；
其他情况下，x ♡ y = x + x + y - x - x。
和 ◇，规则如下：
实数域上，x ◇ y = x - 1 - 5 + y / 5。
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 ◇ 10 ♡ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 1 ◇ 10 ♡ 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 = y + abs(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 a... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 △，规则如下：
当x是5的倍数时，x △ y = x * y；
其他情况下，x △ y = y - x * y * x。
和 ⊕，规则如下：
实数域上，x ⊕ y = 5 / y - x * x + x。
和 ▽，规则如下：
当x小于y时，x ▽ y = x △ x / y / y；
其他情况下，x ▽ y = x - x / y + x - x。
运算优先级：▽ > ** = △ > * = / = % = ⊕ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊕ 6 ⊕ 6 △ 8 ▽ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1735.881944",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 6 ⊕ 6 △ 8 ▽ 7",
"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 = abs(x * y).
and □, the rules are as follows:
when the sum of x and y is odd, x □ y = y ☆ x + y;
otherwise, x □ y = x ☆ y * x.
The precedence of operations: ☆ > ** > * = / = % > + = - = □。
Parentheses have the highest priority, and the expressio... | {
"game_data": {
"answer": "28000",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 2 * 1 □ 10 ☆ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x ** y - y.
and ○, the rules are as follows:
when the sum of x and y is odd, x ○ y = x ** y + y;
otherwise, x ○ y = x + y ⊙ x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y + x - y.
The precedence of operations: ○ > ** ... | {
"game_data": {
"answer": "58",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 6 ◇ 1 ○ 8 ○ 6",
"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 = x - x * y。
和 ○，规则如下：
当x是3的倍数时，x ○ y = x + y - y - x + y；
其他情况下，x ○ y = y * x - 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: 7 ☆ 3 ○ 3 ** 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1136.419753",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ☆ 3 ○ 3 ** 4",
"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都是偶数时，x ☆ y = y + x；
其他情况下，x ☆ y = y * y ** 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 △ 4 ☆ 5 / 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "195.3125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 4 ☆ 5 / 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x + y * 4 * 4。
和 ○，规则如下：
实数域上，x ○ y = x ♡ 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 ♡ 7 ○ 4 - 1 * 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "112",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 7 ○ 4 - 1 * 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
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