env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x + abs(x - y)。
和 □，规则如下：
当y是偶数时，x □ y = y ♢ (x + y)；
其他情况下，x □ y = x - y - y * y。
和 ⊕，规则如下：
当x小于y时，x ⊕ y = y * y + y - x；
其他情况下，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: 1 ⊕ 3 ♢ 9 ♢ 5 □ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊕ 3 ♢ 9 ♢ 5 □ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = y * y - y / x.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + y ⊙ y / x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x * y.
The precedence of operations: ⊙ > ** > * = / = % = ⊕ = ⊗ > + = -。
Parenth... | {
"game_data": {
"answer": "35.852941",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ⊗ 3 ⊙ 6 ⊕ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"... |
logic-v2 | 定义 ◎，规则如下：
当x和y都是奇数时，x ◎ y = y + 5 - x + y - 1；
其他情况下，x ◎ y = x + x + x + y * x。
和 ⊙，规则如下：
实数域上，x ⊙ y = abs(y - x * x) + y。
运算优先级：** = ◎ = ⊙ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ◎ 4 * 9 ⊙ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5670",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ◎ 4 * 9 ⊙ 5",
"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 * (y) + y + x * y。
和 ♡，规则如下：
当x小于y时，x ♡ y = x + y - y * (y / y)；
其他情况下，x ♡ y = x + 5 * y - 5 - 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: 1 □ 1 - 10 ♡ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 1 - 10 ♡ 5",
"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 even, x ☆ y = y + y + x;
otherwise, x ☆ y = y - x * 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 expr... | {
"game_data": {
"answer": "44",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♢ 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 = 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: 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊕, the rules are as follows:
when x is even, x ⊕ y = x + (y) + y * y;
otherwise, x ⊕ y = y * x * x * x.
and ⊗, the rules are as follows:
when x is equal to y, x ⊗ y = x * y - x * x;
otherwise, x ⊗ y = x + y - (y) ⊕ x.
and ▽, the rules are as follows:
when x is a multiple of 5, x ▽ y = x * y - y ⊗ y;
ot... | {
"game_data": {
"answer": "111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊕ 1 ▽ 9",
"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 = x + y ** y;
otherwise, x △ y = y - x - x.
The precedence of operations: ** > * = / = % = △ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 - 5 △ ... | {
"game_data": {
"answer": "9.555556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 - 5 △ 5 / 9",
"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 * y / x - y ** x.
and ○, the rules are as follows:
on the real number field, x ○ y = y + y + y - x / y.
The precedence of operations: ◎ > ** = ○ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parenthes... | {
"game_data": {
"answer": "-46862.499936",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 6 ◎ 5",
"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 = y + x * 5。
和 △，规则如下：
实数域上，x △ y = x □ y。
运算优先级：** > * = / = % > + = - = □ = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 △ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "47",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ♢，规则如下：
当x和y的和是偶数时，x ♢ y = y + x * x；
其他情况下，x ♢ y = x / y。
和 □，规则如下：
当x等于y时，x □ y = y + 3 * y ♢ x；
其他情况下，x □ y = y + x * x + x。
和 ○，规则如下：
实数域上，x ○ y = y - 5 * 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 ○ 6 □ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "11",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 6 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ▽，规则如下：
当x大于y时，x ▽ y = 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: 2 ▽ 8 + 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 8 + 3",
"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和y都是偶数时，x □ y = (5 - x) * y * x；
其他情况下，x □ y = 2 ** y + 3 * x * y。
和 ▽，规则如下：
实数域上，x ▽ y = x □ x ** y - x。
运算优先级：▽ > ** = □ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ▽ 1 - 9 □ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-77",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 1 - 9 □ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nestin... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = 1 * y * x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y ◎ x * x.
The precedence of operations: ◇ > ** = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "16800",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◎ 3 ◎ 10 ◇ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nes... |
logic-v2 | 定义 ☆，规则如下：
当x大于y时，x ☆ y = y - (x) + y；
其他情况下，x ☆ y = y * x - 1。
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: 6 / 7 ☆ 8 % 7 ⊕ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5.857143",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 / 7 ☆ 8 % 7 ⊕ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y - x - x + x + x。
和 ▽，规则如下：
当y是奇数时，x ▽ y = x + x / x ⊕ x / y；
其他情况下，x ▽ y = y / y + x + y + x。
和 ⊙，规则如下：
实数域上，x ⊙ y = y + y - x * abs(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 ▽ 5 ⊕ 2 ⊙ 7 ▽ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "31",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 5 ⊕ 2 ⊙ 7 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nes... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + y / x.
and △, the rules are as follows:
on the real number field, x △ y = x ⊕ y + 2 * 5.
and ☆, the rules are as follows:
when x is odd, x ☆ y = (x) △ x + y * x;
otherwise, x ☆ y = y - abs(x * y * y).
The precedence of operations: △ > ⊕ =... | {
"game_data": {
"answer": "13.769231",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 2 ⊕ 10",
"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 = 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: 10
Please fill your final answe... | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": nu... |
logic-v2 | 定义 ♢，规则如下：
当x是偶数时，x ♢ y = x * y；
其他情况下，x ♢ y = (x + x - y)。
和 ⊙，规则如下：
当x和y都是偶数时，x ⊙ y = y + (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。
运算优先级：⊗ > ** = ♢ > * = / = % = ⊙ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 ♢ 6 ⊙ 10 ⊗ 6 + 2 * 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-22.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ♢ 6 ⊙ 10 ⊗ 6 + 2 * 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": nul... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + y * y * y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = 3 + y + x * 5 + 3.
and □, the rules are as follows:
on the real number field, x □ y = abs(x - y + x + x).
The precedence of operations: ⊙ = ◎ > ** = □ > * = / = %... | {
"game_data": {
"answer": "373",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 □ 10 ⊙ 4 ◎ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ☆, the rules are as follows:
when y is even, x ☆ y = y * x * y;
otherwise, x ☆ y = y - x - y.
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 parenthe... | {
"game_data": {
"answer": "0.987654",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 - 4 ▽ 9 ☆ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | Define ◇, the rules are as follows:
when the sum of x and y is odd, x ◇ y = x + y;
otherwise, 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 express... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define □, the rules are as follows:
when x and y are both even, x □ y = 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 - 1 * x + 2 + y.
and ♡, the rules are as follows:
when x is odd, x ♡ y = x * x - x + y + y;
otherwise, x ♡ y = (x) ▽ y.
... | {
"game_data": {
"answer": "-57",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ▽ 2 □ 7 ♡ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = 3 + y - x * y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y * x ◎ y + y.
The precedence of operations: ◎ > ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "-17",
"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 + 3 * x.
and ◇, the rules are as follows:
when the sum of x and y is even, x ◇ y = y - x - 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": "-119",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 1 △ 9 ◇ 8",
"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 and y are both even, x ☆ y = y + x - y - y + x;
otherwise, x ☆ y = y + abs(y / x).
and ○, 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, a... | {
"game_data": {
"answer": "15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ○ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ◎，规则如下：
当x是奇数时，x ◎ y = y * x + y；
其他情况下，x ◎ y = abs(x + y) * 1。
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: 4 ◎ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "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 | 定义 ◇，规则如下：
当x小于y时，x ◇ y = x ** y - y + x + y；
其他情况下，x ◇ y = x - y * y + y + 2。
和 ☆，规则如下：
当x等于y时，x ☆ y = abs(2) + 5 - x / y * 1；
其他情况下，x ☆ y = y - x + x ◇ y - y。
和 ⊕，规则如下：
实数域上，x ⊕ y = x * x + y - 2。
运算优先级：☆ > ** = ◇ = ⊕ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ⊕ 4 ☆ 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 ⊕ 4 ☆ 2",
"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 - y * x。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 △ 4 + 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 △ 4 + 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + y.
and ♡, the rules are as follows:
when x and y are both odd, x ♡ y = x * y + x;
otherwise, x ♡ y = x / y.
The precedence of operations: ♡ > ** = ⊙ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the p... | {
"game_data": {
"answer": "2.626528",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊙ 3 ** 6 ♡ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = x - (y / x)。
运算优先级：** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y * x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = 1 * y * x * x.
The precedence of operations: ◎ > ** > * = / = % > + = - = ⊗。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "64",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊙, the rules are as follows:
when x is a multiple of 5, x ⊙ y = y - x ** x ** x;
otherwise, x ⊙ y = y - y * y + x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = y + x + y + abs(x - y).
and ◎, the rules are as follows:
when x is odd, x ◎ y = y + (x) * y * x + x;
otherwise, x ◎ y = 4... | {
"game_data": {
"answer": "60",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ◎ 8 ♡ 5 ⊙ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ◇，规则如下：
当x和y都是奇数时，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: 4 % 9 ◇ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 % 9 ◇ 3",
"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y是3的倍数时，x △ y = y + x - (x)；
其他情况下，x △ y = x - y / x + x。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y + y * x - y.
and □, the rules are as follows:
when y is a multiple of 5, x □ y = x * x * y * x;
otherwise, x □ y = x - x - 4 ** y.
The precedence of operations: ** > * = / = % = ♡ = □ > + = -。
Parentheses have the highest priority, and the ex... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♡ 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：
当x等于y时，x ⊕ y = abs(x + y + y)；
其他情况下，x ⊕ y = y * x - x + x。
和 ☆，规则如下：
当x是奇数时，x ☆ y = (y * y + x)；
其他情况下，x ☆ y = y * x ** abs(3)。
和 ⊗，规则如下：
实数域上，x ⊗ y = 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: 8 ☆ 3 ⊕ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9216",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 3 ⊕ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define ▽, the rules are as follows:
when y is a multiple of 3, x ▽ y = x * y - y;
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 expression... | {
"game_data": {
"answer": "27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ▽ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ▽，规则如下：
当x等于y时，x ▽ y = x - y - x；
其他情况下，x ▽ y = (x * y)。
运算优先级：** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ▽ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y * y - x.
and ♢, the rules are as follows:
when the sum of x and y is even, x ♢ y = x □ y - x;
otherwise, x ♢ y = x + y.
The precedence of operations: ♢ > □ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "0",
"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 | Define ○, the rules are as follows:
when y is a multiple of 3, x ○ y = x / y;
otherwise, x ○ y = x ** y.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 ○ 3... | {
"game_data": {
"answer": "1.259921",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ○ 3 * 1 / 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
logic-v2 | 定义 ◎，规则如下：
实数域上，x ◎ y = y - 2 + x + y + x。
和 ☆，规则如下：
实数域上，x ☆ y = y + x + y + y * 2。
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: 1 ◎ 4 ☆ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "40",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◎ 4 ☆ 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是奇数时，x ○ y = x + y；
其他情况下，x ○ y = x - y - y。
运算优先级：** > * = / = % > + = - = ○。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ○ 4 % 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 4 % 3",
"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 * y + x * x。
和 ◇，规则如下：
当x是5的倍数时，x ◇ y = x - y ⊙ y ** y；
其他情况下，x ◇ y = x / 3 * y - 1。
和 □，规则如下：
当x是偶数时，x □ y = y + x ⊙ x * 4；
其他情况下，x □ y = x * x ◇ y / x。
运算优先级：□ > ** = ⊙ > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ⊙ 1 ◇ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-5742",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 1 ◇ 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 = abs(x) + y * 1 - x + y；
其他情况下，x ♢ y = y / x + y - y。
和 ⊙，规则如下：
实数域上，x ⊙ y = (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 ⊙ 7 ♢ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.087719",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 7 ♢ 5",
"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。
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 ▽ 4 / 7 ☆ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.35102",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 4 / 7 ☆ 5",
"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 - x.
and △, the rules are as follows:
on the real number field, x △ y = y * x * y + x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y ** 4 / abs(x) + 5.
The precedence of operations: ⊙ > ⊗ > ** = △ > * = / = % > ... | {
"game_data": {
"answer": "25184.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 8 ⊙ 7 △ 9",
"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 + x - y.
and ◎, the rules are as follows:
on the real number field, x ◎ y = y □ y - x.
The precedence of operations: ◎ > ** = □ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◎ 5 □ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ⊗, the rules are as follows:
when x is a multiple of 3, x ⊗ y = y * abs(x) - y;
otherwise, x ⊗ y = y - y / x.
and ☆, the rules are as follows:
on the real number field, x ☆ y = (x * y ⊗ 3).
and △, the rules are as follows:
when y is odd, x △ y = y - y * x;
otherwise, x △ y = y + x - y.
The precedence o... | {
"game_data": {
"answer": "3.688889",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 6 ☆ 7 ⊗ 4 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = y + 5 - 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: 3 ** 7 * 4 ▽ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9.999428",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ** 7 * 4 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y - (y * x) - x。
和 ▽，规则如下：
实数域上，x ▽ y = x ** x + x - y。
运算优先级：□ > ▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 * 2 % 3 □ 1 ▽ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-12.00064",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 * 2 % 3 □ 1 ▽ 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 a multiple of 5, x ▽ y = y - abs(x / y);
otherwise, x ▽ y = y + x + y.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expre... | {
"game_data": {
"answer": "14",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 + 5 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ⊙，规则如下：
实数域上，x ⊙ y = y + x * y。
和 ◎，规则如下：
当x是奇数时，x ◎ y = x / y * x * y ⊙ y；
其他情况下，x ◎ y = y / y - x ⊙ x。
和 ▽，规则如下：
当x大于y时，x ▽ y = x + y；
其他情况下，x ▽ y = x - x ⊙ 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: 6 ▽ 9 ◎ 2 ⊙ 3 ◎ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "619.512195",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 9 ◎ 2 ⊙ 3 ◎ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ♢，规则如下：
当y是5的倍数时，x ♢ y = (y + y + x) + x；
其他情况下，x ♢ y = x * x - abs(y * y) - y。
和 ⊙，规则如下：
实数域上，x ⊙ y = y - x - x。
和 ○，规则如下：
当x和y的和是奇数时，x ○ y = x - y ♢ x + y；
其他情况下，x ○ y = 5 - 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: 6 ○ 10 ⊙ 6 * 3 ♢ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-250",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ○ 10 ⊙ 6 * 3 ♢ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"... |
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 = y + x * x。
和 ⊗，规则如下：
实数域上，x ⊗ y = abs(y + x)。
运算优先级：** > * = / = % = ⊗ > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ◎ 1 ⊗ 6 * 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 1 ⊗ 6 * 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ⊗，规则如下：
当x是奇数时，x ⊗ y = y + x * 1；
其他情况下，x ⊗ y = (y - x + x)。
和 △，规则如下：
实数域上，x △ y = x * y - x + y。
和 ◇，规则如下：
实数域上，x ◇ y = x * y ⊗ (y * x)。
运算优先级：⊗ > ◇ > ** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 1 ◇ 8 ⊗ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "53",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 1 ◇ 8 ⊗ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | 定义 ▽，规则如下：
当x和y的和是奇数时，x ▽ y = 1 ** x - y；
其他情况下，x ▽ y = y * x。
运算优先级：** > * = / = % = ▽ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ▽ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ☆，规则如下：
当y是5的倍数时，x ☆ y = y + 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: 3 ☆ 8 ◎ 9 ☆ 9 ◎ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8100",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ☆ 8 ◎ 9 ☆ 9 ◎ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = y * y + 2 + x / 2.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * x □ x / y * y.
The precedence of operations: □ = ⊕ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parenthese... | {
"game_data": {
"answer": "95035.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 10 ⊕ 9",
"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) * 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: 1 * 9 ▽ 4 % 1
Please fil... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 * 9 ▽ 4 % 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x / y。
和 ▽，规则如下：
实数域上，x ▽ y = abs(y) + x。
和 ⊕，规则如下：
当y是奇数时，x ⊕ y = x * y - (y)；
其他情况下，x ⊕ y = y - x * y。
运算优先级：⊕ > ** > * = / = % = ▽ > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ▽ 1 ⊕ 2 ⊗ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "1.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ▽ 1 ⊕ 2 ⊗ 5",
"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 3, x ▽ y = y * x - y;
otherwise, x ▽ y = x ** (x - 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... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ▽ 5 % 1 % 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ⊙, the rules are as follows:
when y is a multiple of 3, x ⊙ y = 1 / x + y / 5 - 5;
otherwise, x ⊙ y = 5 / x + x + y - y.
and ☆, the rules are as follows:
on the real number field, x ☆ y = y - x + y + x + y.
The precedence of operations: ☆ > ⊙ > ** > * = / = % > + = -。
Parentheses have the highest priority,... | {
"game_data": {
"answer": "-3.675",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "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:
on the real number field, x ♢ y = 2 - y * x - y + (x).
and ◇, the rules are as follows:
on the real number field, x ◇ y = x - y - x + y - x.
and ○, the rules are as follows:
on the real number field, x ○ y = 5 - y / x.
The precedence of operations: ♢ = ◇ > ** > * = / = % = ○ > ... | {
"game_data": {
"answer": "14.716981",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♢ 7 ○ 5 ◇ 9 * 3",
"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 = x * y + x + y - x;
otherwise, x □ y = y + 3 - x - y / 4.
and ♡, the rules are as follows:
on the real number field, x ♡ y = x / x + x □ y * x.
The precedence of operations: □ > ** > * = / = % = ♡ > + = -。
Parentheses have the highest priority, and the ex... | {
"game_data": {
"answer": "-0.75",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 3 □ 7 □ 4",
"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 a multiple of 3, x ⊙ y = y + 2 + y * x;
otherwise, x ⊙ y = y + 4 + abs(x) - x.
and ▽, the rules are as follows:
when the sum of x and y is even, x ▽ y = y / x * 4 / 3;
otherwise, x ▽ y = y - y ** x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = ... | {
"game_data": {
"answer": "3.058824",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 + 2 ⊙ 9 ◇ 8 ▽ 6 + 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ☆，规则如下：
当x和y的和是奇数时，x ☆ y = x - y / x - y / y；
其他情况下，x ☆ y = x / 5 + (x - x / y)。
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: 7 ☆ 7 ♡ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "11.9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ☆ 7 ♡ 5",
"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 x is a multiple of 3, x ♡ y = 4 + y / x + x;
otherwise, x ♡ y = y + abs(x / y / y).
and ◇, the rules are as follows:
when y is a multiple of 3, x ◇ y = x * (x) + y;
otherwise, x ◇ y = x - y * x.
The precedence of operations: ♡ = ◇ > ** > * = / = % > + = -。
Parentheses ha... | {
"game_data": {
"answer": "46.24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 5 ◇ 2 ◇ 9 + 4",
"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 even, x ☆ y = x * y - y - 1 - y;
otherwise, x ☆ y = 2 * y + x / x.
and ♡, the rules are as follows:
on the real number field, x ♡ y = 2 * x * y.
The precedence of operations: ☆ > ** = ♡ > * = / = % > + = -。
Parentheses have the highest priority, and the ex... | {
"game_data": {
"answer": "420",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 1 ♡ 7 ♡ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x + y - x.
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 △ 3 ** 3
Please fill your fin... | {
"game_data": {
"answer": "27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 △ 3 ** 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ⊕，规则如下：
当x大于y时，x ⊕ y = y ** x；
其他情况下，x ⊕ y = (x + y) * x。
和 ⊙，规则如下：
实数域上，x ⊙ y = y + y / x。
和 △，规则如下：
实数域上，x △ y = 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 △ 5 ⊕ 7 ⊙ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "8",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 5 ⊕ 7 ⊙ 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 = y * y - y - x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = abs(x * y + y) + x.
The precedence of operations: ♡ = ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses i... | {
"game_data": {
"answer": "20",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 6",
"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 - 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ○，规则如下：
当x和y都是奇数时，x ○ y = x + x - 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: 9 ○ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "26",
"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：
实数域上，x ⊕ y = y + y - x。
和 ♡，规则如下：
实数域上，x ♡ y = 3 ⊕ x * y。
和 ☆，规则如下：
当y是3的倍数时，x ☆ y = x - 1 + 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 ⊕ 10 ♡ 1 ☆ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "189",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊕ 10 ♡ 1 ☆ 8",
"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 * 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 * 1 ◇ 6 - 2
Please fill... | {
"game_data": {
"answer": "250",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 * 1 ◇ 6 - 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 ◎，规则如下：
当x大于y时，x ◎ y = y - y * x + x；
其他情况下，x ◎ y = 2 - x + y * y。
运算优先级：◎ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 - 9 ◎ 9 ◎ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 - 9 ◎ 9 ◎ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ♡，规则如下：
当x和y都是偶数时，x ♡ y = x * y；
其他情况下，x ♡ y = y * x / x * x。
和 ▽，规则如下：
当x等于y时，x ▽ y = y - 4 * y - x - x；
其他情况下，x ▽ y = x + x ♡ y + x。
运算优先级：♡ > ** = ▽ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ♡ 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "63",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ♡ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | 定义 ▽，规则如下：
当y是奇数时，x ▽ y = x - y - y - y；
其他情况下，x ▽ y = x + x - y * x。
和 ○，规则如下：
当x和y的和是偶数时，x ○ y = x - y - 4 + y；
其他情况下，x ○ y = y - x * x。
和 □，规则如下：
实数域上，x □ y = abs(y / x - 5) / y。
运算优先级：○ = □ > ▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 ○ 10 □ 10 ▽ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.388889",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ○ 10 □ 10 ▽ 1",
"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 = 5 - y - x.
and ◇, the rules are as follows:
when y is a multiple of 5, x ◇ y = y * y - x ** y;
otherwise, x ◇ y = x ☆ y + 1 + x.
The precedence of operations: ** = ☆ = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expres... | {
"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：
实数域上，x △ y = x * abs(y)。
和 ⊗，规则如下：
当x是5的倍数时，x ⊗ y = y △ x + y * y + y；
其他情况下，x ⊗ y = (3) + x / 4 △ y * y。
和 □，规则如下：
实数域上，x □ y = x + y + abs(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 □ 3 ⊗ 1 △ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 3 ⊗ 1 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define △, the rules are as follows:
when x is a multiple of 3, x △ y = y - y + x * x;
otherwise, x △ y = x + 2 + 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": "0.138889",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 / 6 △ 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 + y * abs(y - x * x).
and ○, the rules are as follows:
when x is greater than y, x ○ y = y * 1 - x * 2;
otherwise, x ○ y = x - y ⊕ y + y * x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x - x - x + 3 * y.
The preceden... | {
"game_data": {
"answer": "-861",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 1 ⊕ 6 ◇ 6 ○ 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 / y + x - x * 3。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 * 10 ◇ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-90",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 * 10 ◇ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = (y / 5 * x) * x.
and ○, the rules are as follows:
on the real number field, x ○ y = y * x * abs(5 - y).
The precedence of operations: ♡ > ** > * = / = % = ○ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses... | {
"game_data": {
"answer": "18880",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 % 9 ○ 8 ♡ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = x / 1 - 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: 8
Please fill your final an... | {
"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和y都是偶数时，x ○ y = x / y + x；
其他情况下，x ○ y = x * y。
运算优先级：○ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 - 2 ○ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1.2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 - 2 ○ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ☆，规则如下：
实数域上，x ☆ y = y * x + x。
和 ◎，规则如下：
当x和y都是偶数时，x ◎ y = x / y - y；
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: 9 ☆ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "81",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ☆ 8",
"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 - y - y * x / 5;
otherwise, x ○ y = 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 expre... | {
"game_data": {
"answer": "-13",
"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 + x * y * y.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 9 ** 5 / 7 ○ 2
Please fill ... | {
"game_data": {
"answer": "33744.285714",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ** 5 / 7 ○ 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 and y are both even, x ♢ y = y ** abs(x + x);
otherwise, x ♢ y = y + x.
and ♡, the rules are as follows:
when x is greater than y, x ♡ y = y * y - x;
otherwise, x ♡ y = y ♢ x / y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + y ♢ 4.
The prece... | {
"game_data": {
"answer": "31.696938",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 6 ** 5 ♡ 10 ♢ 4",
"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 odd, x ○ y = 4 * y / 3 + x;
otherwise, x ○ y = y * y * x * x + 2.
The precedence of operations: ** > * = / = % > + = - = ○。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression... | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = abs(x) * y * 3.
and ♡, the rules are as follows:
when the sum of x and y is odd, x ♡ y = (x + y);
otherwise, x ♡ y = (x - y) + y.
and ☆, the rules are as follows:
when x is greater than y, x ☆ y = y * y + x;
otherwise, x ☆ y = y + (y) △ x.
... | {
"game_data": {
"answer": "165",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 4 ☆ 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = 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: 3 □ 8 △ 8 + 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 □ 8 △ 8 + 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = 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
Please fill your final answer in... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ◇, the rules are as follows:
on the real number field, x ◇ y = y + x * x.
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 ◇ 2
Please fill your final an... | {
"game_data": {
"answer": "51",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ◇ 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:
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: 9 / 10 ◇ 6 % 9
Please fill your fin... | {
"game_data": {
"answer": "6.9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 / 10 ◇ 6 % 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 x is even, x ◇ y = y + y / 1 ** x * y;
otherwise, x ◇ y = x * y + y - y - y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expr... | {
"game_data": {
"answer": "4984",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 9 ◇ 8 * 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = x + y * abs(y * x)。
和 ♡，规则如下：
实数域上，x ♡ y = x - (x) * y * y。
和 ○，规则如下：
实数域上，x ○ y = y + abs(x * y) - x。
运算优先级：** = ♡ > * = / = % = ○ > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊗ 7 ○ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7630",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊗ 7 ○ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = y - y * x / 5.
and ⊗, the rules are as follows:
when x and y are both odd, x ⊗ y = y ♡ x + x;
otherwise, x ⊗ y = (x) ♡ y * y / y.
The precedence of operations: ♡ > ** = ⊗ > * = / = % > + = -。
Parentheses have the highest priority, and the expre... | {
"game_data": {
"answer": "3.99995",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ** 8 ♡ 9 ⊗ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"n... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.