env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | Define □, the rules are as follows:
when x is a multiple of 3, x □ y = abs(y + y + x / y);
otherwise, x □ y = x - x + y - x + x.
and ⊗, the rules are as follows:
when x is less than y, x ⊗ y = abs(5 ** x / y) + y / y;
otherwise, x ⊗ y = x + 3 * x * y + 4.
The precedence of operations: ⊗ > ** > * = / = % > + = -... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ⊗ 5 ⊗ 8 □ 9",
"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 = 5 - x * y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = 3 ** (x ◎ 4) * y.
The precedence of operations: ◇ > ◎ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calc... | {
"game_data": {
"answer": "32767.997186",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ** 8 ◎ 6 ◇ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y / y * x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 4
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:
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 - x.
and △, the rules are as follows:
when y is even, x △ y = x ⊕ x / y;
otherwise, x △ y = y + x.
The precedence of operations: ⊕ > ▽ > ** > * = / = % > + ... | {
"game_data": {
"answer": "27.166667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 4 * 3 △ 1 / 5 ⊕ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * y / y.
and ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = x + abs(y);
otherwise, x ▽ y = 3 - x ⊗ y.
The precedence of operations: ⊗ = ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression ins... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 4 ⊗ 6 ⊗ 8 % 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) * y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = abs(y - x) * y.
The precedence of operations: ** > * = / = % = ☆ > + = - = ◇。
Parentheses have the highest priority, and the expression inside the parentheses is calc... | {
"game_data": {
"answer": "399",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ☆ 10 ◇ 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 = x + y + x.
and ◇, 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 + y * y.
The precedence of operations: ⊕ > ** > * = / = % = ⊗ > + = - = ◇。
Parentheses hav... | {
"game_data": {
"answer": "1539",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ** 3 ⊗ 1 ** 3 ⊕ 2 ◇ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x - x - x * y / y。
和 ⊙，规则如下：
当x和y都是奇数时，x ⊙ y = y □ x - 3 / 1；
其他情况下，x ⊙ y = x - y - x - x * x。
运算优先级：⊙ > ** > * = / = % = □ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 7 ⊙ 9 □ 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 □ 7 ⊙ 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:
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: 2 ◇ 1
Please fill your final an... | {
"game_data": {
"answer": "4",
"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 | Define ○, the rules are as follows:
when x is odd, x ○ y = (y) - x - y;
otherwise, x ○ y = x - 4 + y - y.
The precedence of operations: ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 10 -... | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 - 9 % 7 ○ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define ☆, the rules are as follows:
when y is even, x ☆ y = x / x * y;
otherwise, x ☆ y = y * x + x.
and ♡, the rules are as follows:
when x is even, x ♡ y = x * 3 ☆ y;
otherwise, x ♡ y = x + y ☆ x.
The precedence of operations: ♡ > ** = ☆ > * = / = % > + = -。
Parentheses have the highest priority, and the expr... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 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 = y + x。
和 ⊙，规则如下：
当y是奇数时，x ⊙ y = x / y + abs(4)；
其他情况下，x ⊙ y = 2 + y / x。
和 ○，规则如下：
当x小于y时，x ○ 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: 6 ○ 4 ♢ 5 ⊙ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 4 ♢ 5 ⊙ 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 - x * x。
和 ○，规则如下：
当x和y都是偶数时，x ○ y = y - x / x + y / x；
其他情况下，x ○ y = y ♢ x。
和 ◇，规则如下：
当x小于y时，x ◇ y = x * 2 * (y + y)；
其他情况下，x ◇ y = y - 5 + 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 ◇ 7 ○ 5 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-105",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◇ 7 ○ 5 ♢ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = 5 * y + y + x + y.
and ♢, the rules are as follows:
on the real number field, x ♢ y = y - y - x + y * y.
The precedence of operations: ♡ > ** > * = / = % = ♢ > + = -。
Parentheses have the highest priority, and the expression inside the parenthese... | {
"game_data": {
"answer": "-7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * y + x - x.
and ◇, the rules are as follows:
when x and y are both odd, x ◇ y = 3 + 2 - x / y ⊗ x;
otherwise, x ◇ y = x * 2 * 3 - x * y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x - y / 5.
The precedence of operat... | {
"game_data": {
"answer": "78.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊗ 9 ⊕ 7 ◇ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ⊕, the rules are as follows:
when x is a multiple of 3, x ⊕ y = y + abs(x - y) + y + y;
otherwise, x ⊕ y = y - x + x - y + x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x - x - y * 5.
and △, the rules are as follows:
on the real number field, x △ y = y * x - x * x.
The precedence ... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊕ 8 ⊗ 10 △ 6 % 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = 1 + x - 5 + y * 3.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x + y.
The precedence of operations: △ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calcula... | {
"game_data": {
"answer": "21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 8",
"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 = x - y - y + y + x；
其他情况下，x ⊗ y = y - x + y。
和 ◎，规则如下：
当x大于y时，x ◎ y = abs(x / x) / y；
其他情况下，x ◎ y = x + y ⊗ x + x + y。
运算优先级：⊗ = ◎ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ◎ 8 / 1 ⊗ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.307692",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 8 / 1 ⊗ 7",
"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 / x * y。
和 ○，规则如下：
实数域上，x ○ y = 2 ⊗ y * x。
和 □，规则如下：
当y是5的倍数时，x □ y = x + x ○ y + x；
其他情况下，x □ y = 1 + 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 ⊗ 7 - 1 □ 2 ○ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊗ 7 - 1 □ 2 ○ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ⊗，规则如下：
当x和y的和是偶数时，x ⊗ y = (2 * 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 + x。
运算优先级：⊕ > ** > * = / = % = ⊗ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ⊗ 9 ⊕ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "90",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊗ 9 ⊕ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ♡, the rules are as follows:
when x is a multiple of 3, x ♡ y = (x + 1) ** y;
otherwise, x ♡ y = x + y.
and ⊕, the rules are as follows:
when y is a multiple of 5, x ⊕ y = x - y - y;
otherwise, x ⊕ y = y + x - x.
The precedence of operations: ♡ > ** = ⊕ > * = / = % > + = -。
Parentheses have the highest p... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 3 ⊕ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x / (x * y * y) + 1.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x - y - abs(y * x) ** y.
and ○, the rules are as follows:
on the real number field, x ○ y = y * x - abs(4 + 5).
The precedence of operations: ○ > ** = ☆ > *... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 8 ☆ 1",
"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 / 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 ◇ 7 - 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "43.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 7 - 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
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 = y ⊕ y + x - x + y。
和 ▽，规则如下：
实数域上，x ▽ y = 3 * x - y。
运算优先级：⊕ > ** > * = / = % = ○ > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ▽ 5 ○ 3 ⊕ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-158",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 5 ○ 3 ⊕ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | Define ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = x - 2 * y;
otherwise, x ⊙ y = 5 - y - x.
and △, the rules are as follows:
on the real number field, x △ y = y ⊙ x + y.
and ⊗, the rules are as follows:
when the sum of x and y is odd, x ⊗ y = x * 5 ⊙ y;
otherwise, x ⊗ y = x △ y + y.
T... | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 5 ⊙ 2 ⊗ 1 △ 9 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ▽, the rules are as follows:
when x is even, x ▽ y = y ** x + y - y;
otherwise, x ▽ y = (y + x + x) + y - x.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expres... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 5 * 5 % 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = y + 4 * 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 ○ 6
Please fill your fina... | {
"game_data": {
"answer": "24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 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 is greater than y, x ⊗ y = y + x / y - x;
otherwise, x ⊗ y = x * 3 + y * (y).
and ◎, the rules are as follows:
when the sum of x and y is odd, x ◎ y = x + x * y - y;
otherwise, x ◎ y = x * abs(1 * y).
and △, the rules are as follows:
on the real number field, x △ y = ... | {
"game_data": {
"answer": "-857.729167",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 5 ◎ 3 △ 10 ⊗ 6 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": nu... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x - 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 fina... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y * y + x。
和 □，规则如下：
实数域上，x □ y = abs(y + x)。
和 ♡，规则如下：
当x等于y时，x ♡ y = x + y；
其他情况下，x ♡ y = abs(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: 8 ⊕ 5 □ 2 ♡ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "171",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊕ 5 □ 2 ♡ 1",
"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 = abs(x) + x ** y。
和 ♡，规则如下：
当x和y的和是奇数时，x ♡ y = y + x - y * y + y；
其他情况下，x ♡ y = x ⊙ x - y。
和 ⊕，规则如下：
当x等于y时，x ⊕ y = x + y / y ♡ y；
其他情况下，x ⊕ y = 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: 5 ♡ 9 ⊕ 8 ⊙ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "49920",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ♡ 9 ⊕ 8 ⊙ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = x + x + 5 * y + x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = y + x + x + y / y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y + 3 - 4 ♢ 5 - x.
The precedence of operations: ⊗ > ** > * = / = % = ♢ ... | {
"game_data": {
"answer": "-143",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 9 ⊗ 6 ▽ 4 - 10 ⊗ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = 1 - y + (y) * x.
and ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = y - y * (x - y);
otherwise, x ▽ y = 3 ⊕ y / y / x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y + x - x.
The precedence of operations... | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 3 ⊕ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y - y + abs(x * x + y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = y - x * x ** (y - x).
The precedence of operations: ▽ > ** = ☆ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the pa... | {
"game_data": {
"answer": "29",
"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：
实数域上，x ○ y = x / x * x + (x) - y。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ○ 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 ○ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth... |
logic-v2 | Define ○, the rules are as follows:
when the sum of x and y is even, x ○ y = y + x - x + y;
otherwise, x ○ y = y * x + 5 + y.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of ... | {
"game_data": {
"answer": "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:
when x is a multiple of 5, x ⊗ y = x + y;
otherwise, x ⊗ y = y * y - x.
and ♡, the rules are as follows:
when x is even, x ♡ y = abs(y) * x;
otherwise, x ♡ y = y + x - x.
The precedence of operations: ** = ⊗ = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and ... | {
"game_data": {
"answer": "23",
"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和y都是奇数时，x ☆ y = 1 - x + x * y + 5；
其他情况下，x ☆ y = y - x - y - 2 ** x。
和 □，规则如下：
当x等于y时，x □ y = y - y / x - x；
其他情况下，x □ y = x + y ☆ y - y。
运算优先级：** = □ > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ☆ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 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都是奇数时，x △ y = y + abs(x - 2 + 2 * 5)；
其他情况下，x △ y = x * y * x + x * x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 □，规则如下：
当y是5的倍数时，x □ y = x + (y)；
其他情况下，x □ y = x + y。
和 ○，规则如下：
实数域上，x ○ y = (1 □ 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 □ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 □ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define △, the rules are as follows:
when y is even, x △ y = x / 4 - 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: 10 △ 2
Pl... | {
"game_data": {
"answer": "0.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth... |
logic-v2 | Define □, the rules are as follows:
when y is a multiple of 5, x □ y = x - x ** y + 3 * x;
otherwise, x □ y = y ** x - y / x.
and ⊗, the rules are as follows:
when y is odd, x ⊗ y = x + x + y + x □ y;
otherwise, x ⊗ y = x + y * y - y □ (x).
The precedence of operations: □ > ** > * = / = % > + = - = ⊗。
Parenthes... | {
"game_data": {
"answer": "-32715.216667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 2 □ 3 - 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 = x + y * 1 - y - abs(2).
and ▽, the rules are as follows:
on the real number field, x ▽ y = abs(x + x - x) * y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y + x - 4 + y / 2.
The precedence of operations: ▽ > ⊙ > ** > * = ... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊕ 2 ⊙ 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:
when x is a multiple of 3, x ⊗ y = x * x - abs(y) - y;
otherwise, x ⊗ y = y / y * x * y.
and ◇, the rules are as follows:
when x is a multiple of 3, x ◇ y = y + x - 1 ⊗ x;
otherwise, x ◇ y = x * y + 3.
The precedence of operations: ** = ⊗ = ◇ > * = / = % > + = -。
Parentheses ... | {
"game_data": {
"answer": "99",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 4 ◇ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ◎, the rules are as follows:
when the sum of x and y is odd, x ◎ y = y ** 1 + x;
otherwise, x ◎ y = y + x * abs(y - y).
and ⊙, the rules are as follows:
when x and y are both odd, x ⊙ y = x * y - x ◎ x;
otherwise, x ⊙ y = y * y - x ◎ (y).
The precedence of operations: ◎ = ⊙ > ** > * = / = % > + = -。
Pare... | {
"game_data": {
"answer": "65",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 8 ⊙ 8 + 9",
"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 = abs(y * x) + x - x.
and △, the rules are as follows:
on the real number field, x △ y = 5 + x * 4 + y.
The precedence of operations: ◎ > ** > * = / = % > + = - = △。
Parentheses have the highest priority, and the expression inside the parentheses i... | {
"game_data": {
"answer": "39",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 1 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 □，规则如下：
当y是偶数时，x □ y = x * 3 / x + 4 - y；
其他情况下，x □ y = y - y / x - x。
和 ⊗，规则如下：
实数域上，x ⊗ y = y / x - abs(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: 9 - 7 ⊗ 10 □ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4.025974",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 - 7 ⊗ 10 □ 7",
"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 - x - x)。
和 △，规则如下：
实数域上，x △ y = x - 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: 9 △ 3 ☆ 6 * 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-90",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 3 ☆ 6 * 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ☆, the rules are as follows:
when the sum of x and y is odd, x ☆ y = x - x / y - x - 4;
otherwise, x ☆ y = x - x * x ** x * y.
and ♡, the rules are as follows:
when y is a multiple of 3, x ♡ y = x - x - 4 ☆ 3 + y;
otherwise, x ♡ y = x + x ☆ x + y - x.
The precedence of operations: ** = ♡ > * = / = % > + ... | {
"game_data": {
"answer": "-5.25",
"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_dept... |
logic-v2 | 定义 △，规则如下：
当x小于y时，x △ y = y * x ** 3；
其他情况下，x △ y = x * abs(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 △ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1944",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 + 3 △ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define △, the rules are as follows:
when y is a multiple of 5, x △ y = x + x / y * (y);
otherwise, x △ y = y * (x / y + 2 + x).
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value o... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 1 / 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = abs(y) * x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x ♢ y * x.
and ♡, the rules are as follows:
when y is a multiple of 5, x ♡ y = abs(5) - x - y;
otherwise, x ♡ y = y + y - x.
The precedence of operations: ** > * =... | {
"game_data": {
"answer": "-4090",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♡ 3 ⊙ 8 ♢ 2 ** 7 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x / x + x + y。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 / 7 ○ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 / 7 ○ 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3的倍数时，x ⊙ y = y + x + y - y / x；
其他情况下，x ⊙ y = x - 4 - x + x / y。
和 ⊕，规则如下：
当x和y都是奇数时，x ⊕ y = x - y ⊙ y - x + y；
其他情况下，x ⊕ y = x + y。
和 ♡，规则如下：
实数域上，x ♡ y = y / x / x ⊕ y。
运算优先级：⊙ > ♡ > ** > * = / = % > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♡ 2 ⊕ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6.125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 2 ⊕ 4",
"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。
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 = 5 + y + x - y。
和 △，规则如下：
实数域上，x △ y = x * y * x / y。
和 ○，规则如下：
当x是奇数时，x ○ y = y ** y * x - y / y；
其他情况下，x ○ y = x △ 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: 8 ○ 10 △ 3 ⊙ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2814",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ○ 10 △ 3 ⊙ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ⊗, the rules are as follows:
when x is a multiple of 3, x ⊗ y = y * x + 2 * y;
otherwise, x ⊗ y = y + abs(x + y / x).
and ◇, the rules are as follows:
on the real number field, x ◇ y = y + x.
and ♡, the rules are as follows:
when x is even, x ♡ y = x * y - x;
otherwise, x ♡ y = 3 * 1 - x * y ⊗ y.
The p... | {
"game_data": {
"answer": "-45.543011",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊗ 10 ◇ 4 ♡ 2",
"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 + 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: 9 - 6 ▽ 1 - 8
Please ... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 - 6 ▽ 1 - 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ◎, the rules are as follows:
when y is a multiple of 3, x ◎ y = 2 - x - y;
otherwise, x ◎ y = (y - x * x) - x * x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - y / x ◎ y.
The precedence of operations: ◎ > ** > * = / = % > + = - = ⊙。
Parentheses have the highest priority, and the e... | {
"game_data": {
"answer": "-51.545455",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊙ 10 + 6 ◎ 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 = (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: 8 △ 9 * 10 △ 6
Please fill yo... | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 9 * 10 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y + x + x - x。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ▽ 4 ▽ 7 ▽ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 4 ▽ 7 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ⊕，规则如下：
当y是5的倍数时，x ⊕ y = y / x + x - 5 - x；
其他情况下，x ⊕ y = x - 1 - y * y。
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 = (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: 9 ♡ 2 ⊕ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-2.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♡ 2 ⊕ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = x * y / 5 * x。
和 ◎，规则如下：
当x和y都是奇数时，x ◎ y = 3 / y ♡ x + 2；
其他情况下，x ◎ y = y ♡ x / y + y。
运算优先级：◎ > ** = ♡ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♡ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "12.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth... |
logic-v2 | Define ○, the rules are as follows:
when y is a multiple of 3, x ○ y = x + abs(5 * y - y * x);
otherwise, x ○ y = x * abs(x + y * y).
The precedence of operations: ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the v... | {
"game_data": {
"answer": "29",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 + 8 ○ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ○, the rules are as follows:
when x is a multiple of 5, x ○ y = x * y + 1 * y;
otherwise, x ○ y = y - 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": "0.052632",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 / 5 / 8 ○ 7",
"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和y都是奇数时，x ▽ y = abs(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 ▽ 2 - 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "60",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 2 - 10",
"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是奇数时，x ⊗ y = y * y - x；
其他情况下，x ⊗ y = x + y。
和 △，规则如下：
实数域上，x △ y = x - x + y + x。
和 ◎，规则如下：
当x和y都是偶数时，x ◎ y = y * x ⊗ 3 / x；
其他情况下，x ◎ y = x + 5 + 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: 7 ⊗ 4 ◎ 4 △ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "33",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 4 ◎ 4 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 △，规则如下：
当x是偶数时，x △ y = y * x；
其他情况下，x △ y = y + x + y。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 △ 8 * 10 △ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2300",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 8 * 10 △ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ♡, the rules are as follows:
when x is less than y, x ♡ y = y * y - x;
otherwise, x ♡ y = abs(y) ** y + x.
and ○, the rules are as follows:
on the real number field, x ○ y = x * y ♡ y.
The precedence of operations: ♡ > ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "90",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 1 ○ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ☆, the rules are as follows:
when y is odd, x ☆ y = x * x * x - x + y;
otherwise, x ☆ y = x * abs(x) * x * 5 / y.
and ◎, the rules are as follows:
when x is equal to y, x ◎ y = x - y + y ☆ y;
otherwise, x ◎ y = x * y + x ☆ y.
The precedence of operations: ☆ > ** > * = / = % = ◎ > + = -。
Parentheses have ... | {
"game_data": {
"answer": "1017",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 7 ☆ 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:
when x is even, x ▽ y = y - y * x;
otherwise, x ▽ y = x - 5 + 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 ... | {
"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 + 4 * y - x.
and ⊙, the rules are as follows:
when x is greater than y, x ⊙ y = (y / x + y) - y;
otherwise, x ⊙ y = x - 2 / y + x.
The precedence of operations: ⊙ > ** = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the ex... | {
"game_data": {
"answer": "15.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ⊗, the rules are as follows:
when y is a multiple of 3, x ⊗ y = y * y ** x - y + y;
otherwise, x ⊗ y = y + x - y * 4 + 4.
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 = x + x ◇ y + y + y.
The precede... | {
"game_data": {
"answer": "17.125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 8 ⊗ 6 ◇ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = y / 5 - x.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y ⊗ y * x.
and △, the rules are as follows:
when y is a multiple of 3, x △ y = x ◎ (y / x);
otherwise, x △ y = (y) * x * y.
The precedence of operations: △ > ** > *... | {
"game_data": {
"answer": "24.8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 8 ⊗ 8 + 4 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y * 3 + x + y.
and ☆, the rules are as follows:
when the sum of x and y is odd, x ☆ y = y * y ◎ x - x;
otherwise, x ☆ y = (y * 5 / y + x).
The precedence of operations: ** > * = / = % > + = - = ◎ = ☆。
Parentheses have the highest priority, and ... | {
"game_data": {
"answer": "77",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 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 = y - x - y；
其他情况下，x △ y = y + y * x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 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：
实数域上，x ☆ y = x - y / y + x。
和 ○，规则如下：
实数域上，x ○ y = 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 * 2 ☆ 10 ○ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "23.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 * 2 ☆ 10 ○ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ◇, the rules are as follows:
when y is even, x ◇ y = y - 5 * 5 + x * y;
otherwise, x ◇ y = y + x - x * x.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expressio... | {
"game_data": {
"answer": "0.714286",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 / 2 ◇ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define □, the rules are as follows:
when the sum of x and y is odd, x □ y = y - x - y * y;
otherwise, x □ y = x - y / y.
and ⊕, the rules are as follows:
when y is odd, x ⊕ y = y + x + x;
otherwise, x ⊕ y = x ** 2 * 4 - y.
The precedence of operations: □ > ** > * = / = % > + = - = ⊕。
Parentheses have the highes... | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 9 % 3 ⊕ 6 + 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"ne... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = x * y - 3 + y.
and ☆, the rules are as follows:
when x is a multiple of 5, x ☆ y = x ♢ y;
otherwise, x ☆ y = y + y * (x).
and ⊙, the rules are as follows:
when x is less than y, x ⊙ y = x + y ☆ x / y;
otherwise, x ⊙ y = y + x - y * y.
The p... | {
"game_data": {
"answer": "-1462",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 5 ☆ 8 ⊙ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = x + (x ** x) - y。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ○ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * y - y / x.
and ○, the rules are as follows:
on the real number field, x ○ y = (x ⊙ x) + y + x - x.
The precedence of operations: ⊙ > ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses ... | {
"game_data": {
"answer": "62.857143",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ▽，规则如下：
当x和y的和是奇数时，x ▽ y = x + abs(x * y * y)；
其他情况下，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: 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:
when x is a multiple of 3, x □ y = (x) - y * y;
otherwise, x □ y = y * x + x.
and ○, the rules are as follows:
on the real number field, x ○ y = y * x - y.
The precedence of operations: □ > ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 □ 6 ○ 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5的倍数时，x ◇ y = x * y - y / x + (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: 8 * 3 ◇ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "52528",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 * 3 ◇ 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 = 5 - y * x - abs(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: 3 △ 5 * 7 △ 4
Plea... | {
"game_data": {
"answer": "620",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 5 * 7 △ 4",
"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 * x * x.
and ☆, the rules are as follows:
when x is less than y, x ☆ y = 5 - x / y;
otherwise, x ☆ y = y * x.
The precedence of operations: ☆ > ** > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression inside the p... | {
"game_data": {
"answer": "25.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 / 3 ♡ 2 ☆ 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 * 2 * x / y;
otherwise, x ◎ y = (y + x + y) * x.
and ♢, the rules are as follows:
on the real number field, x ♢ y = y ◎ x / y + 4.
The precedence of operations: ◎ > ♢ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression i... | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 6 % 7 ◎ 10 ♢ 2",
"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 * x * x。
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: 7 ☆ 8 ○ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.005102",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ☆ 8 ○ 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 = y + y * (x - x * x).
and ⊕, the rules are as follows:
when the sum of x and y is even, x ⊕ y = y + y ◎ x ** 1;
otherwise, x ⊕ y = y ◎ x.
The precedence of operations: ** = ◎ > * = / = % = ⊕ > + = -。
Parentheses have the highest priority, and th... | {
"game_data": {
"answer": "-88",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ○, the rules are as follows:
when x is odd, x ○ y = x + y + (2 * x / 3);
otherwise, x ○ y = (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 e... | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ♡，规则如下：
实数域上，x ♡ y = 4 * y + 4 + x。
和 ⊗，规则如下：
实数域上，x ⊗ y = y ♡ x - y。
运算优先级：♡ > ** > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ♡ 9 ⊗ 7 - 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "165",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ♡ 9 ⊗ 7 - 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 = x - y - abs(x)。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 △ 8 / 1 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 8 / 1 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ▽, the rules are as follows:
when x is a multiple of 5, x ▽ y = x * x + x + x - y;
otherwise, x ▽ y = 3 + 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 o... | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ** 1 ▽ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = x - (y * y).
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 5 ○ 6 * 2
Please fill your fi... | {
"game_data": {
"answer": "-62",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 6 * 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | Define ⊕, the rules are as follows:
when x is odd, x ⊕ y = abs(x * y * y);
otherwise, x ⊕ y = y / y * x.
and ◎, 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 = x - y * x.
The precedence of operations: ▽ > ⊕ > ** > * = / = ... | {
"game_data": {
"answer": "-0.142857",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 2 ◎ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define □, the rules are as follows:
when x is less than y, x □ y = abs(4) * x / y + y * x;
otherwise, x □ y = x - abs(y * x - x).
and ♢, the rules are as follows:
on the real number field, x ♢ y = (x) + y □ x - x - x.
The precedence of operations: ** > * = / = % = □ = ♢ > + = -。
Parentheses have the highest prior... | {
"game_data": {
"answer": "-156.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 + 5 □ 6 ♢ 4",
"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 = y + x + 4 + y.
and ♡, the rules are as follows:
when x is greater than y, x ♡ y = x + x * y □ x;
otherwise, x ♡ y = (y - x * y □ x).
The precedence of operations: ** > * = / = % = ♡ > + = - = □。
Parenthe... | {
"game_data": {
"answer": "66",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♡ 1 □ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x - y * x / y - x.
and ◇, the rules are as follows:
when x is a multiple of 3, x ◇ y = x * y / x - abs(y) - x;
otherwise, x ◇ y = x + y / x * x.
The precedence of operations: ☆ = ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority... | {
"game_data": {
"answer": "7",
"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：
实数域上，x ☆ y = abs(y * x - 2) - 3 - x。
和 ⊙，规则如下：
当y是偶数时，x ⊙ y = (y + x - 4 - 3 + x)；
其他情况下，x ⊙ y = x + y ☆ x。
运算优先级：⊙ > ** > * = / = % > + = - = ☆。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ☆ 10 ⊙ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "88",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ☆ 10 ⊙ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
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