env stringclasses 1
value | prompt stringlengths 119 673 | extra dict |
|---|---|---|
logic-v2 | 定义 ⊕，规则如下：
当x是3的倍数时，x ⊕ y = abs(y * 5) - 3 - 3 - x；
其他情况下，x ⊕ y = x + x - x + y。
和 ◎，规则如下：
当y是3的倍数时，x ◎ y = x / abs(y * x) * 1；
其他情况下，x ◎ y = x ⊕ y * x / y。
和 ⊗，规则如下：
实数域上，x ⊗ y = y + x ** 2 - 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 ⊗ 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "90",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 8 ⊗ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ♡, the rules are as follows:
when the sum of x and y is even, x ♡ y = y - x / y - 1 - y;
otherwise, x ♡ y = x + (y * y) + x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x - y - x - y + x.
The precedence of operations: ♡ = ◇ > ** > * = / = % > + = -。
Parentheses have the highest prior... | {
"game_data": {
"answer": "-27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ** 6 - 3 ♡ 6 ◇ 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的和是奇数时，x △ y = 2 - x + x - x * y；
其他情况下，x △ y = y / x + y - x - x。
运算优先级：** > * = / = % > + = - = △。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 % 1 ** 2 △ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 % 1 ** 2 △ 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：
实数域上，x △ y = y + x。
和 ⊗，规则如下：
实数域上，x ⊗ y = x - x △ y。
运算优先级：** = ⊕ = △ = ⊗ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 7 ⊗ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 7 ⊗ 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：
实数域上，x ♡ y = y / x + 3。
和 △，规则如下：
实数域上，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: 10 △ 7 + 2 ♡ 8 * 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-13.227181",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 7 + 2 ♡ 8 * 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ○, the rules are as follows:
when x and y are both even, x ○ y = y - y + x - 1;
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 e... | {
"game_data": {
"answer": "21",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ○ 5",
"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 * x) + y.
The precedence of operations: ◇ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 3
Please fill your final answ... | {
"game_data": {
"answer": "3",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ▽, the rules are as follows:
when y is odd, x ▽ y = y - x + y - 3;
otherwise, x ▽ 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 expression: 9 ▽ 5
... | {
"game_data": {
"answer": "-2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = y * y + x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = x / y - 3.
The precedence of operations: ◎ = ▽ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "5.666667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◎ 5 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 ▽，规则如下：
实数域上，x ▽ y = 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 △，规则如下：
当x是3的倍数时，x △ y = y - (x - y) / 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: 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x + y。
和 △，规则如下：
实数域上，x △ y = x - y * y。
运算优先级：□ = △ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 □ 10 △ 4 - 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-15",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 10 △ 4 - 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define □, the rules are as follows:
on the real number field, x □ y = x * y.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + x * y / x.
The precedence of operations: □ > ** > * = / = % = ⊕ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated ... | {
"game_data": {
"answer": "22",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊕ 8 □ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ○，规则如下：
实数域上，x ○ y = 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 ○ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "131.714286",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "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:
when the sum of x and y is even, x ◇ y = y + y * x;
otherwise, x ◇ y = y * x + x.
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expr... | {
"game_data": {
"answer": "12",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ◇ 9 % 7 + 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ⊙, the rules are as follows:
on the real number field, x ⊙ y = x + x + y - 3.
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = x + x * y ⊙ y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = x / y / x * x ⊙ y.
The precedence of operations: ⊗ > ** > * = / = % = ⊙ = ⊕ > + ... | {
"game_data": {
"answer": "111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 8 ⊗ 4 ⊙ 1 - 1",
"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 - (2 * y).
and ○, the rules are as follows:
when x and y are both even, x ○ y = x - x * y;
otherwise, x ○ y = 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 - 4.
The prece... | {
"game_data": {
"answer": "0.7125",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ○ 8 △ 1 △ 10 ⊕ 3 △ 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 odd, x □ y = x - y + y * x;
otherwise, x □ y = y + y + y / x.
and ☆, the rules are as follows:
when x is equal to y, x ☆ y = x - x * y - 5;
otherwise, x ☆ y = y * 2 - x.
and △, the rules are as follows:
when y is odd, x △ y = 1 - x / y;
otherwise,... | {
"game_data": {
"answer": "25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 △ 2 □ 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x是奇数时，x ♢ y = y - x - x；
其他情况下，x ♢ y = x + abs(4 + y)。
和 ♡，规则如下：
实数域上，x ♡ y = y + y + x。
和 □，规则如下：
当x和y都是奇数时，x □ y = y - 4 * x；
其他情况下，x □ y = abs(x / y)。
运算优先级：♢ = □ > ** > * = / = % > + = - = ♡。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ♢ 3 ♡ 8 □ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10.6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ♢ 3 ♡ 8 □ 10",
"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 = x * 5 + x / y。
和 ○，规则如下：
当x等于y时，x ○ y = y + x △ x + y - y；
其他情况下，x ○ y = (y) + y * x。
和 ⊗，规则如下：
当y是3的倍数时，x ⊗ y = x / x * y + x；
其他情况下，x ⊗ y = 2 / 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 ⊗ 8 ○ 7
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "65",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊗ 8 ○ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define ☆, the rules are as follows:
when y is odd, x ☆ y = x + y;
otherwise, x ☆ y = x / 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 inside the parenthes... | {
"game_data": {
"answer": "-15.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ☆ 10 ⊕ 7 ⊕ 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 = x - x + y + y。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 1 △ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 5",
"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 = abs(x) + x + y。
运算优先级：▽ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = 1 / x * 3 * y + 1。
和 ⊙，规则如下：
实数域上，x ⊙ y = 4 ⊕ y - x + y。
和 ▽，规则如下：
实数域上，x ▽ y = x / y ⊙ (y - y) - y。
运算优先级：⊕ = ⊙ > ** > * = / = % > + = - = ▽。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ⊕ 3 ▽ 2 ⊙ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-6.56",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 3 ▽ 2 ⊙ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ◎, the rules are as follows:
when x is greater than y, x ◎ y = x - y + y * x + x;
otherwise, x ◎ y = x * 5 + y * x.
and ⊙, the rules are as follows:
when the sum of x and y is even, x ⊙ y = (x - x) + x ◎ y * x;
otherwise, x ⊙ y = y - x * y.
The precedence of operations: ** > * = / = % = ◎ = ⊙ > + = -。
Pa... | {
"game_data": {
"answer": "-128",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 2 ◎ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define ♢, the rules are as follows:
on the real number field, x ♢ y = y + x.
and ▽, the rules are as follows:
on the real number field, x ▽ y = (1 + x ♢ y).
and ♡, the rules are as follows:
on the real number field, x ♡ y = x - y - y.
The precedence of operations: ♢ > ** = ▽ = ♡ > * = / = % > + = -。
Parentheses h... | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ▽ 8 ♡ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 △，规则如下：
当x和y的和是奇数时，x △ y = x - y * 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: 4 % 8 △ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "65536",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 % 8 △ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = y - x + (y) + y * y.
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 8
Please fill your fi... | {
"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 = abs(x ** y - x)。
运算优先级：△ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 △ 1 △ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 △ 1 △ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dept... |
logic-v2 | Define ◇, the rules are as follows:
when x is less than y, x ◇ y = y * y + x;
otherwise, x ◇ y = x ** y * x.
The precedence of operations: ** = ◇ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2... | {
"game_data": {
"answer": "27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 5 % 9 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = y / x + x * y + x。
和 ☆，规则如下：
当x小于y时，x ☆ y = y + y + x；
其他情况下，x ☆ y = x * y + abs(x - x + y)。
和 ◇，规则如下：
当y是5的倍数时，x ◇ y = x - x * x * y + x；
其他情况下，x ◇ y = 1 - 1 / y + x。
运算优先级：** = ♢ = ☆ > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 5 ◇ 6 ☆ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "5.952381",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ◇ 6 ☆ 3",
"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 = 4 + x * x / y.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y / x * 2 - y.
The precedence of operations: ** = ⊗ > * = / = % = □ > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is cal... | {
"game_data": {
"answer": "-48.455556",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 10 * 9 ⊗ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ☆，规则如下：
当x是5的倍数时，x ☆ y = y - x + x；
其他情况下，x ☆ y = (y / x)。
和 □，规则如下：
实数域上，x □ y = y / x。
运算优先级：□ > ** > * = / = % = ☆ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 / 9 □ 10 ☆ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.962963",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 9 □ 10 ☆ 8",
"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 * (3 * y * x)。
和 ▽，规则如下：
实数域上，x ▽ y = abs(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: 10 % 10 ◎ 1 - 1 ▽ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 % 10 ◎ 1 - 1 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x * y * x。
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: 10 □ 9 ♢ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "900",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 □ 9 ♢ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x / x + y.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 2 △ 5
Please fill your final an... | {
"game_data": {
"answer": "6",
"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 | Define □, the rules are as follows:
when y is a multiple of 5, x □ y = y + x - x;
otherwise, x □ y = x / y * x - x.
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y - (x ** x).
The precedence of operations: ** > * = / = % = □ = ⊗ > + = -。
Parentheses have the highest priority, and the expressi... | {
"game_data": {
"answer": "1850.228571",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ⊗ 5 □ 7 / 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | 定义 ◇，规则如下：
当x是5的倍数时，x ◇ y = (y * 3) + x；
其他情况下，x ◇ y = 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: 2 ◇ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "50",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ◇ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ♡, the rules are as follows:
on the real number field, x ♡ y = (y - x - x).
and ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * x.
The precedence of operations: ** = ⊕ > * = / = % > + = - = ♡。
Parentheses have the highest priority, and the expression inside the parentheses is calculated fi... | {
"game_data": {
"answer": "24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ♡ 10 ⊕ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_de... |
logic-v2 | 定义 ⊕，规则如下：
实数域上，x ⊕ y = y * y - 1 * x + 4。
和 ⊙，规则如下：
实数域上，x ⊙ y = y - x - y ⊕ x。
和 ◇，规则如下：
实数域上，x ◇ y = x - 1 + 4 + y + y。
运算优先级：◇ > ⊙ > ** > * = / = % > + = - = ⊕。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◇ 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": "3 ◇ 6 ⊕ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x / (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: 10 △ 3
Please fill your f... | {
"game_data": {
"answer": "-2.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 △ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 □，规则如下：
当x和y的和是偶数时，x □ y = y - y - x + x - x；
其他情况下，x □ y = y + x。
和 ♡，规则如下：
当y是3的倍数时，x ♡ y = abs(y) + x；
其他情况下，x ♡ y = x * y / y。
运算优先级：□ > ♡ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 ♡ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 ♡ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": ... |
logic-v2 | Define △, the rules are as follows:
when x is even, x △ y = 3 * 5 - x - y;
otherwise, x △ y = y + y * x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 1 △ 5... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 △ 5 △ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dept... |
logic-v2 | 定义 ◇，规则如下：
当x和y都是奇数时，x ◇ y = (y - x * y - 1 + 1)；
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: 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = y * (x - 1).
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
Please fill your final ... | {
"game_data": {
"answer": "24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ▽ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ⊕, the rules are as follows:
when y is odd, x ⊕ y = x + 3 - y - y;
otherwise, x ⊕ y = x / y - abs(y).
and ▽, the rules are as follows:
on the real number field, x ▽ y = y / x * x.
and ◇, the rules are as follows:
on the real number field, x ◇ y = y / x.
The precedence of operations: ** = ⊕ = ▽ > * = / = ... | {
"game_data": {
"answer": "-1.4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 10 ▽ 4 ⊕ 5",
"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 and y are both even, x □ y = y + x - 4;
otherwise, x □ y = 2 * y * x.
and ⊙, the rules are as follows:
when x is odd, x ⊙ y = 5 * x - y;
otherwise, x ⊙ y = y □ x * 2.
The precedence of operations: □ > ** = ⊙ > * = / = % > + = -。
Parentheses have the highest priority, a... | {
"game_data": {
"answer": "13",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊙ 6 □ 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：
实数域上，x ◎ y = y + (y) / x。
和 ⊙，规则如下：
当x小于y时，x ⊙ y = y - abs(x - y)；
其他情况下，x ⊙ y = x / y * x。
运算优先级：◎ > ⊙ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 ⊙ 6 ◎ 4
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "10.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊙ 6 ◎ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ♢，规则如下：
当x小于y时，x ♢ y = y - x - x - x；
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 = y ♢ (y + x - y)；
其他情况下，x □ y = y - x / y ♢ y。
和 ◎，规则如下：
当x是奇数时，x ◎ y = y - x □ x * 2；
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: 3 □ 9 ◎ 1 ♢ 8
请将最终答案填入... | {
"game_data": {
"answer": "-1.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 □ 9 ◎ 1 ♢ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesti... |
logic-v2 | 定义 ◎，规则如下：
当x是奇数时，x ◎ y = x - y - y - y；
其他情况下，x ◎ y = 2 + x * y - 2。
和 ⊗，规则如下：
当x是3的倍数时，x ⊗ y = x / y + x - 4；
其他情况下，x ⊗ y = x - 3 ◎ 5 - y。
运算优先级：◎ > ** > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 9 ◎ 3 ⊗ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-4",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ◎ 3 ⊗ 2",
"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 = y ** x.
and △, the rules are as follows:
when x is a multiple of 5, x △ y = x + y;
otherwise, x △ y = abs(y) - x + y.
and ○, the rules are as follows:
when x is greater than y, x ○ y = y * x △ x / x;
otherwise, x ○ y = x / y + y ⊕ y.
The pr... | {
"game_data": {
"answer": "1024",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ○ 4 ⊕ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 □，规则如下：
当x是3的倍数时，x □ y = (y + y * x) + x + y；
其他情况下，x □ y = y - y * 5 * y - x。
和 △，规则如下：
当x等于y时，x △ y = y * 5 - y □ x - x；
其他情况下，x △ y = (x - 2 □ x) - y。
运算优先级：△ > ** = □ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 □ 4 □ 6 △ 8 % 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 □ 4 □ 6 △ 8 % 9",
"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 = x * y;
otherwise, x △ y = y + y + x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7
... | {
"game_data": {
"answer": "7",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 ◇，规则如下：
当x和y都是偶数时，x ◇ y = abs(1 * 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: 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:
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: 1 ◇ 1
Please fill your fina... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◇ 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 and y are both odd, x ⊙ y = y + x;
otherwise, x ⊙ y = abs(x + y) + y.
and □, the rules are as follows:
when x and y are both odd, x □ y = x + y;
otherwise, x □ y = y + (x) + 2.
and ♡, the rules are as follows:
on the real number field, x ♡ y = (x) * y * x.
The preced... | {
"game_data": {
"answer": "1214",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ♡ 6 □ 4 ⊙ 7",
"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 and y are both odd, x ○ y = 4 + x * x + x + y;
otherwise, x ○ 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 t... | {
"game_data": {
"answer": "95",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ○ 1 % 8",
"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大于y时，x ⊗ y = x * x - y + x；
其他情况下，x ⊗ y = x * y。
和 ◎，规则如下：
实数域上，x ◎ y = y - x * 3。
和 □，规则如下：
实数域上，x □ y = 5 - 2 / 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 ⊗ 6 - 2 □ 9 ◎ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "50.333333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊗ 6 - 2 □ 9 ◎ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = y + x - 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 ▽ 8 + 9
Please fill your fina... | {
"game_data": {
"answer": "17",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 8 + 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 □，规则如下：
当x是奇数时，x □ y = x * x * y；
其他情况下，x □ y = x + y。
和 ⊗，规则如下：
实数域上，x ⊗ y = x □ x * y。
运算优先级：⊗ > □ > ** > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 7 □ 1 % 9 ⊗ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "49",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 □ 1 % 9 ⊗ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting... |
logic-v2 | Define ▽, the rules are as follows:
when x is a multiple of 3, x ▽ y = y / x + x / y + x;
otherwise, x ▽ y = x + x - x / y * y.
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 + 3 * x + x ** y.
The precedence of opera... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ▽ 4 □ 10",
"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 3, x ☆ y = x * y / y;
otherwise, x ☆ y = x * y - x * x.
and ◎, the rules are as follows:
when y is odd, x ◎ y = y ☆ 3 * x * 3;
otherwise, x ◎ y = x / 5 / y + 2.
The precedence of operations: ☆ > ** > * = / = % > + = - = ◎。
Parentheses have the highest ... | {
"game_data": {
"answer": "-30",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 ◎ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | Define ○, the rules are as follows:
when x and y are both odd, x ○ y = abs(y - y) + x;
otherwise, x ○ y = x * 2 * (y).
The precedence of operations: ○ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the exp... | {
"game_data": {
"answer": "169",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ○ 8 + 9",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | 定义 ♡，规则如下：
当x是3的倍数时，x ♡ y = y / x - y；
其他情况下，x ♡ y = abs(x - y / x)。
和 ◎，规则如下：
实数域上，x ◎ y = y ♡ x - y。
运算优先级：♡ > ** > * = / = % > + = - = ◎。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 10 ** 3 ♡ 1 ** 8 ◎ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-1e-06",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ** 3 ♡ 1 ** 8 ◎ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ♢，规则如下：
当x和y的和是奇数时，x ♢ y = y - x - y * y；
其他情况下，x ♢ y = 4 + y + x。
和 △，规则如下：
当x和y都是偶数时，x △ y = y + y + x * 1；
其他情况下，x △ y = x * y * abs(1 - y)。
运算优先级：△ > ** = ♢ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 6 △ 1 ♢ 1 ** 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 △ 1 ♢ 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：
实数域上，x △ y = x + x - y。
运算优先级：** > * = / = % = △ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 4 △ 6 / 9
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "0.222222",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 △ 6 / 9",
"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 = x * 5 * x + 4 - y;
otherwise, x □ y = y * x - x.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = (1) □ y + y / x.
The precedence of operations: ** = ⊙ > * = / = % = □ > + = -。
Parentheses have the highest priority, and... | {
"game_data": {
"answer": "0.5",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 □ 10 ⊙ 7 % 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = y * abs(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 * 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 □ 3 ▽ 1 / 9 ▽ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "20.111111",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 □ 3 ▽ 1 / 9 ▽ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = y * y + 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 △ 9
Please fill your fina... | {
"game_data": {
"answer": "117",
"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：
实数域上，x ◇ y = y + x + (x) * y + x。
运算优先级：** > * = / = % > + = - = ◇。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 3 ◇ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth":... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = x - y * y.
and ⊕, the rules are as follows:
when x is a multiple of 3, x ⊕ y = x / (y) ☆ x;
otherwise, x ⊕ y = x * y - y.
The precedence of operations: ☆ > ** = ⊕ > * = / = % > + = -。
Parentheses have the highest priority, and the expression in... | {
"game_data": {
"answer": "1",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ⊕ 1 ** 7 ☆ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nestin... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = x - x + 1 / y。
和 ♡，规则如下：
当x是5的倍数时，x ♡ y = x + x □ y；
其他情况下，x ♡ y = x - y ** 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 □ 4 ♡ 9 ♡ 10
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-0.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 4 ♡ 9 ♡ 10",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = y + x - y * x * x.
and ⊙, the rules are as follows:
when the sum of x and y is odd, x ⊙ y = x + y * y * x - x;
otherwise, x ⊙ y = (x + y * y).
The precedence of operations: ** > * = / = % = ☆ = ⊙ > + = -。
Parentheses have the highest priority, ... | {
"game_data": {
"answer": "-15477",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ⊙ 8 ☆ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | Define ○, the rules are as follows:
on the real number field, x ○ y = y * x * y * y.
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
Please fill your final an... | {
"game_data": {
"answer": "2",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth": null... |
logic-v2 | Define ⊗, the rules are as follows:
on the real number field, x ⊗ y = (y / x ** y - y) + y.
and □, the rules are as follows:
on the real number field, x □ y = y * x ⊗ x - x + y.
and ⊕, the rules are as follows:
when y is odd, x ⊕ y = x - 4 ⊗ y * x + x;
otherwise, x ⊕ y = y + x + 3 + (5 - x).
The precedence of o... | {
"game_data": {
"answer": "2e-06",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊕ 1 ⊗ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | Define ☆, the rules are as follows:
on the real number field, x ☆ y = 3 - y ** x * 1 * y.
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 parenthes... | {
"game_data": {
"answer": "-1021",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 % 1 ☆ 5 ♡ 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 greater than y, x ⊕ y = y + x + y - x ** y;
otherwise, x ⊕ y = y + x + x + x + y.
and ◇, the rules are as follows:
on the real number field, x ◇ y = x ⊕ x - y + 5.
and ☆, the rules are as follows:
when x is less than y, x ☆ y = x ⊕ x - y / x - y;
otherwise, x ☆ y = ... | {
"game_data": {
"answer": "-2641",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 8 ☆ 6 ◇ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nest... |
logic-v2 | 定义 ⊗，规则如下：
实数域上，x ⊗ y = 2 - 1 * 4 * y - x。
和 □，规则如下：
实数域上，x □ y = x * x / y ⊗ 4 * 5。
和 ☆，规则如下：
当x和y的和是奇数时，x ☆ y = y * y □ x * y * x；
其他情况下，x ☆ y = y / x ⊗ x - y + y。
运算优先级：** = □ = ☆ > * = / = % > + = - = ⊗。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ☆ 5 ⊗ 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "16203",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ☆ 5 ⊗ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_... |
logic-v2 | Define ▽, the rules are as follows:
on the real number field, x ▽ y = y + x / 1 / y - 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: 3 * 3 ▽ 4
Please fill y... | {
"game_data": {
"answer": "8.25",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 * 3 ▽ 4",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_d... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y + x - y.
and ▽, the rules are as follows:
on the real number field, x ▽ y = y + x * y.
and □, the rules are as follows:
on the real number field, x □ y = x ⊕ y * x.
The precedence of operations: ⊕ > ** > * = / = % = ▽ > + = - = □。
Parentheses... | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "4 □ 4 ⊕ 3 ▽ 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting... |
logic-v2 | 定义 ○，规则如下：
当x小于y时，x ○ y = y * x；
其他情况下，x ○ y = x + 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: 8 + 4 ○ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "18",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 + 4 ○ 2",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_dep... |
logic-v2 | 定义 ♡，规则如下：
当x是奇数时，x ♡ y = y ** abs(5 + x) + y；
其他情况下，x ♡ y = y - x - x + 4。
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: 10 ⊗ 1 ♡ 3 ♡ 3 + 1
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "42",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊗ 1 ♡ 3 ♡ 3 + 1",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"ne... |
logic-v2 | Define □, the rules are as follows:
when x is a multiple of 5, x □ y = (1 - y + x) - x;
otherwise, x □ y = (y / x) - x.
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 express... | {
"game_data": {
"answer": "-119.511745",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 / 10 □ 5 □ 7 ○ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
... |
logic-v2 | Define △, the rules are as follows:
on the real number field, x △ y = x / y - x.
The precedence of operations: ** = △ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 7 △ 6
Please fill your final an... | {
"game_data": {
"answer": "-5.833333",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 △ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_... |
logic-v2 | 定义 ○，规则如下：
当y是5的倍数时，x ○ y = x + x + y - (x - y)；
其他情况下，x ○ y = 2 - 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
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "6",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_depth": null... |
logic-v2 | 定义 □，规则如下：
实数域上，x □ y = (x + y) / x。
和 ⊕，规则如下：
当x和y都是偶数时，x ⊕ y = x * 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: 3 □ 10 ⊕ 5
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "2.166667",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 □ 10 ⊕ 5",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nest... |
logic-v2 | Define ◎, the rules are as follows:
when y is a multiple of 3, x ◎ y = y / y + x;
otherwise, x ◎ y = y * x ** y.
and ⊙, the rules are as follows:
on the real number field, x ⊙ y = y - x * 3.
The precedence of operations: ⊙ > ** = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the expression ins... | {
"game_data": {
"answer": "0.0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ** 7 ⊙ 2 ◎ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesti... |
logic-v2 | Define ♢, the rules are as follows:
when x is equal to y, x ♢ y = x / (y + x);
otherwise, x ♢ y = y - x * 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 * y.
The precedence of operations: ♢ > ** = ◎ > * =... | {
"game_data": {
"answer": "0.001953",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊙ 1 ♢ 10 * 10 ◎ 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 * (2 ** 3)。
和 ◎，规则如下：
实数域上，x ◎ y = y + x - x * y。
和 ⊕，规则如下：
当y是3的倍数时，x ⊕ y = y * 4 - 5 ⊗ x - y；
其他情况下，x ⊕ y = y / x + 5 * 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 ⊕ 3 ◎ 4 ⊗ 8 % 6
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "174",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "10 ⊕ 3 ◎ 4 ⊗ 8 % 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"n... |
logic-v2 | 定义 ♢，规则如下：
实数域上，x ♢ y = x * y。
和 ◎，规则如下：
当x大于y时，x ◎ y = x ♢ 3 - x ** y；
其他情况下，x ◎ y = x + x * y ♢ x * x。
和 ○，规则如下：
当y是奇数时，x ○ y = x * x * x ♢ y；
其他情况下，x ○ y = y * abs(y + x / 2)。
运算优先级：○ > ♢ > ** > * = / = % = ◎ > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 8 ◎ 9 ♢ 2
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "9224",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "8 ◎ 9 ♢ 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 = x + y * x.
The precedence of operations: △ > ** > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the expression: 6 - 8 △ 8
Please fill your fina... | {
"game_data": {
"answer": "-66",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 - 8 △ 8",
"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 y is even, x ▽ y = x - x - (y * y + y);
otherwise, x ▽ y = x * y * x - y.
The precedence of operations: ** = ▽ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses is calculated first.
Please calculate the value of the express... | {
"game_data": {
"answer": "-42",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "3 ▽ 6",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
logic-v2 | 定义 ⊕，规则如下：
当x小于y时，x ⊕ y = x * y + y ** x；
其他情况下，x ⊕ y = x + (y * 4 / x)。
和 ♢，规则如下：
当x和y的和是奇数时，x ♢ y = 4 ⊕ (y / x - 2)；
其他情况下，x ♢ y = 1 ⊕ (y - x / x / 3)。
和 ⊗，规则如下：
当x小于y时，x ⊗ y = x * x / x ♢ y + 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: 7 ⊕ 1 /... | {
"game_data": {
"answer": "0.213687",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "7 ⊕ 1 / 8 ⊗ 8 ♢ 7",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
... |
logic-v2 | 定义 ⊕，规则如下：
当x和y都是偶数时，x ⊕ y = y + x；
其他情况下，x ⊕ y = x + x / y。
和 ▽，规则如下：
当x是3的倍数时，x ▽ y = x / y * y；
其他情况下，x ▽ y = x * 2 + y。
和 ♡，规则如下：
实数域上，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: 6 ⊕ 10 ♡ 8
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "24",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "6 ⊕ 10 ♡ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ⊕, the rules are as follows:
on the real number field, x ⊕ y = y * 1 / x - y - x.
and ◎, the rules are as follows:
when x and y are both even, x ◎ y = x / abs(y / x);
otherwise, x ◎ y = y * x / y ** y ** y.
and □, the rules are as follows:
when x is equal to y, x □ y = x * x ⊕ y * y;
otherwise, x □ y = ... | {
"game_data": {
"answer": "0",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "1 □ 6 ** 5 ◎ 6 * 5 ⊕ 1",
"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 + x * x；
其他情况下，x ☆ y = (y) * x + y。
和 ⊗，规则如下：
当x是偶数时，x ⊗ y = y * (x + x)；
其他情况下，x ⊗ y = y - x ☆ x。
运算优先级：⊗ > ** = ☆ > * = / = % > + = -。
括号具有最高优先级，先计算括号内的表达式。
请计算表达式的值: 2 ☆ 3 ⊗ 3
请将最终答案填入\boxed{}中。 | {
"game_data": {
"answer": "-27",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "2 ☆ 3 ⊗ 3",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "chinese",
"n_types": null,
"nesting_de... |
logic-v2 | Define ◎, the rules are as follows:
on the real number field, x ◎ y = x - x * abs(y).
and □, the rules are as follows:
when y is a multiple of 3, x □ y = x / x ◎ y;
otherwise, x □ y = y * y - x.
The precedence of operations: □ > ** = ◎ > * = / = % > + = -。
Parentheses have the highest priority, and the expression... | {
"game_data": {
"answer": "-637",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 □ 10 ◎ 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 the sum of x and y is even, x ♢ y = y - abs(x) ** x;
otherwise, x ♢ y = y * x - y.
and □, the rules are as follows:
when y is a multiple of 5, x □ y = x - y + x;
otherwise, x □ y = y * x.
and ◇, the rules are as follows:
when x is greater than y, x ◇ y = x + x - abs(y)... | {
"game_data": {
"answer": "16",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ♢ 2 □ 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 * y + abs(y).
and ⊗, the rules are as follows:
on the real number field, x ⊗ y = y ☆ x * y + x.
The precedence of operations: ⊗ > ** = ☆ > * = / = % > + = -。
Parentheses have the highest priority, and the expression inside the parentheses i... | {
"game_data": {
"answer": "-124",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "5 ⊗ 9 ☆ 6",
"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 + 2.
and ⊕, the rules are as follows:
when x is a multiple of 3, x ⊕ y = 5 - x + y ☆ y;
otherwise, x ⊕ y = x / (y).
The precedence of operations: ** = ⊕ > * = / = % > + = - = ☆。
Parentheses have the highest priority, and the expressio... | {
"game_data": {
"answer": "-26",
"difficulty": 1,
"gpt_response": "",
"metadata": {
"closing_sequence": null,
"expression": "9 ⊕ 8",
"fill_length": null,
"full_sequence": null,
"is_solvable": null,
"language": "english",
"n_types": null,
"nesting_depth"... |
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