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 - 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: 2 ◇ 9 ♢ 7 * 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "55", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ◇ 9 ♢ 7 * 5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting...
logic-v2
定义 ○,规则如下: 实数域上,x ○ y = x * y / x。 运算优先级:** > * = / = % = ○ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 2 + 1 - 8 ○ 1 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "2", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 + 1 - 8 ○ 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都是奇数时,x ⊕ y = x ** x * y; 其他情况下,x ⊕ y = y - y * x。 和 ♡,规则如下: 当x和y的和是奇数时,x ♡ y = y + x; 其他情况下,x ♡ y = abs(x * y) + y。 和 ▽,规则如下: 当x大于y时,x ▽ y = y - y * x; 其他情况下,x ▽ y = y + x - y。 运算优先级:♡ > ** > * = / = % = ⊕ = ▽ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 5 ♡ 8 ⊕ 2 ▽ 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-24", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ♡ 8 ⊕ 2 ▽ 5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nestin...
logic-v2
定义 ◇,规则如下: 当x和y的和是偶数时,x ◇ y = x - y + x * y; 其他情况下,x ◇ y = 2 - x + 5 * y + 5。 和 ⊕,规则如下: 当x大于y时,x ⊕ y = 3 - y * x ◇ 5 - y; 其他情况下,x ⊕ y = (x) ◇ x + 1 * y * y。 和 ▽,规则如下: 当x和y的和是偶数时,x ▽ y = abs(5 - x - y) - x - y; 其他情况下,x ▽ y = 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...
{ "game_data": { "answer": "158", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ⊕ 8 ◇ 10 ▽ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesti...
logic-v2
Define ☆, the rules are as follows: when x and y are both even, x ☆ y = y / x - y - 5; otherwise, x ☆ y = abs(2 + 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 e...
{ "game_data": { "answer": "6528", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 △ 8 * 1 ☆ 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 = (x - 2) ** y. and △, 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 odd, x ○ y = abs(x + y); otherwise, x ○ y = (x) △ x - y. The precedence of operations: ** ...
{ "game_data": { "answer": "36864", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ○ 2 △ 6", "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 - y * y。 和 ⊕,规则如下: 实数域上,x ⊕ y = y ** x * 3 * y。 和 ▽,规则如下: 实数域上,x ▽ y = y / x / (x) * y。 运算优先级:▽ > ⊙ > ** > * = / = % = ⊕ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 1 + 10 ▽ 7 ⊙ 5 ⊕ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "1.0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 + 10 ▽ 7 ⊙ 5 ⊕ 7", "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 = x + y * x + y * y. The precedence of operations: ** = ▽ > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 10 ▽ 3 Please fill your...
{ "game_data": { "answer": "49", "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_depth"...
logic-v2
定义 ⊙,规则如下: 实数域上,x ⊙ y = x ** x ** 3 - y。 和 ▽,规则如下: 实数域上,x ▽ y = x + y。 和 ♢,规则如下: 实数域上,x ♢ y = y ⊙ (x - x) + y。 运算优先级:** = ⊙ > * = / = % = ▽ = ♢ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 2 ▽ 3 ♢ 1 ⊙ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-2", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ▽ 3 ♢ 1 ⊙ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting...
logic-v2
定义 ⊕,规则如下: 当y是偶数时,x ⊕ y = y + y / abs(x); 其他情况下,x ⊕ y = y + x + x。 和 ⊙,规则如下: 实数域上,x ⊙ y = x - y ⊕ y + 2。 和 △,规则如下: 当x和y都是奇数时,x △ y = 3 / x * y; 其他情况下,x △ y = abs(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: 6 ⊙ 8 / 3 ⊕ 7 △ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-0.04", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ⊙ 8 / 3 ⊕ 7 △ 10", "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 + 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": "16389", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 □ 7 ♡ 2 / 4 / 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 - 4 - y. and □, the rules are as follows: when the sum of x and y is even, x □ y = 1 * x - x ♡ 1 + y; otherwise, x □ y = y - x * x ♡ y. The precedence of operations: ** > * = / = % = ♡ > + = - = □。 Parentheses have the highest priority, a...
{ "game_data": { "answer": "21.555556", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 □ 9", "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是偶数时,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 / 3 ◇ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "0.002", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 / 3 ◇ 10", "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 = x / y - x; 其他情况下,x ☆ y = (y + x * x)。 和 ⊗,规则如下: 实数域上,x ⊗ y = y ☆ x / x。 运算优先级:☆ = ⊗ > ** > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 4 ☆ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-3.6", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 ☆ 10", "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是3的倍数时,x ○ y = 2 + x - 3 + 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: 9 / 3 ○ 6 % 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 / 3 ○ 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是偶数时,x ○ y = y + abs(x); 其他情况下,x ○ y = x + x + y。 运算优先级:** = ○ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "2", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth": null...
logic-v2
定义 ♡,规则如下: 当x大于y时,x ♡ y = y + x - x * y / y; 其他情况下,x ♡ y = y - x / 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: 10 ♡ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "3", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ♡ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth":...
logic-v2
Define ◎, the rules are as follows: when the sum of x and y is odd, x ◎ y = y - y - x + 3; otherwise, x ◎ y = x + y. and ◇, the rules are as follows: when x is a multiple of 5, x ◇ y = y - 3 / x; otherwise, x ◇ y = x + x ◎ x * y. The precedence of operations: ** = ◇ > * = / = % = ◎ > + = -。 Parentheses have the...
{ "game_data": { "answer": "74", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ◎ 4 ◇ 8 ** 1 ◎ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "ne...
logic-v2
Define ◎, the rules are as follows: when y is a multiple of 3, x ◎ y = x / y / y - x + x; otherwise, x ◎ y = y + x - x / y. and ☆, the rules are as follows: on the real number field, x ☆ y = x + x ** y - 5 + y. The precedence of operations: ◎ > ** = ☆ > * = / = % > + = -。 Parentheses have the highest priority, an...
{ "game_data": { "answer": "6", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 % 7 ☆ 6 ◎ 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 - x + y. 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 parentheses is calculated ...
{ "game_data": { "answer": "4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 □ 4 ♢ 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都是奇数时,x ◎ y = y * x - y - y; 其他情况下,x ◎ y = x - x * y。 和 ⊙,规则如下: 实数域上,x ⊙ y = x ◎ y - x - y。 运算优先级:⊙ > ** = ◎ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 3 ◎ 9 ⊙ 3 ** 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "59049", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ◎ 9 ⊙ 3 ** 5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nes...
logic-v2
Define ◇, the rules are as follows: when the sum of x and y is odd, x ◇ y = x - 4 * 3 + y; otherwise, x ◇ y = x - x * (y ** x). The precedence of operations: ** = ◇ > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value o...
{ "game_data": { "answer": "-16380", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 ◇ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_dep...
logic-v2
定义 ⊗,规则如下: 实数域上,x ⊗ y = x / y。 和 ♡,规则如下: 当x是5的倍数时,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: 6 ♡ 5 ⊗ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "0.75", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ♡ 5 ⊗ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_d...
logic-v2
定义 ☆,规则如下: 实数域上,x ☆ y = y - x * y + 3。 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: 10 * 8 ◇ 8 ☆ 10 ◇ 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-11498", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 * 8 ◇ 8 ☆ 10 ◇ 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的和是偶数时,x □ y = 3 + y + x; 其他情况下,x □ y = 3 / x - y - y。 和 ◎,规则如下: 实数域上,x ◎ y = x + y + x。 运算优先级:□ = ◎ > ** > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 7 - 7 □ 1 ◎ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-23", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 - 7 □ 1 ◎ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nestin...
logic-v2
定义 ◎,规则如下: 实数域上,x ◎ y = y * x。 和 ○,规则如下: 当y是偶数时,x ○ y = y * x; 其他情况下,x ○ y = x ◎ 2 * y。 运算优先级:○ > ** = ◎ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 2 ◎ 4 ○ 9 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "144", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ◎ 4 ○ 9", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_de...
logic-v2
Define ○, the rules are as follows: when the sum of x and y is odd, x ○ y = 1 * 4 * x + y * y; otherwise, x ○ y = 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 va...
{ "game_data": { "answer": "97", "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 - 1 * x * y。 和 ◎,规则如下: 实数域上,x ◎ y = x / y * x + y。 运算优先级:** = ☆ = ◎ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 5 ◎ 3 ☆ 2 ☆ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "151.666667", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ◎ 3 ☆ 2 ☆ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, ...
logic-v2
Define ☆, the rules are as follows: when x is odd, x ☆ y = abs(y * 1 + x); otherwise, x ☆ y = y - (x ** x - x). and ⊕, the rules are as follows: on the real number field, x ⊕ y = (y * y) + x * 1. The precedence of operations: ** = ☆ = ⊕ > * = / = % > + = -。 Parentheses have the highest priority, and the expressio...
{ "game_data": { "answer": "15", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ⊕ 2 ☆ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_dep...
logic-v2
Define △, the rules are as follows: when the sum of x and y is odd, x △ y = x - x + y ** x; otherwise, x △ y = x * x - y * x. The precedence of operations: △ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of ...
{ "game_data": { "answer": "81", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 △ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth":...
logic-v2
定义 ♢,规则如下: 实数域上,x ♢ y = 2 / y ** x。 和 ⊙,规则如下: 当y是奇数时,x ⊙ y = x - 2 ♢ y; 其他情况下,x ⊙ y = y + x - x。 和 △,规则如下: 当x和y的和是奇数时,x △ y = 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: 4 △ 7 ⊙ 4 ♢ 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "0.0032", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 △ 7 ⊙ 4 ♢ 5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nes...
logic-v2
定义 ▽,规则如下: 实数域上,x ▽ y = (x / y - x) + x。 和 ♢,规则如下: 当y是3的倍数时,x ♢ y = x ▽ x - y * x - x; 其他情况下,x ♢ y = (x + 1 ▽ 2 - 3 + y)。 和 ◎,规则如下: 当x和y都是偶数时,x ◎ y = (y + y / 1) * y - x; 其他情况下,x ◎ y = (x + 1 + y) - 4 * x。 运算优先级:▽ > ** = ♢ > * = / = % = ◎ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 7 ◎ 8 ♢ 9 ▽ 10 % 10 请将最终答案填入\b...
{ "game_data": { "answer": "6.4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ◎ 8 ♢ 9 ▽ 10 % 10", "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 = x / y - x. and ⊗, the rules are as follows: on the real number field, x ⊗ y = abs(y / x). The precedence of operations: ◎ > ** > * = / = % = ⊗ > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated...
{ "game_data": { "answer": "2.5", "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 x is less than y, x ◎ y = x + x / y + 4 / x; otherwise, x ◎ y = 2 * 2 - y - x - y. and □, the rules are as follows: on the real number field, x □ y = y + y - y ◎ y - x. The precedence of operations: □ > ** = ◎ > * = / = % > + = -。 Parentheses have the highest priority, and...
{ "game_data": { "answer": "3.392702", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 □ 6 ◎ 6 □ 10 / 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和y都是偶数时,x ♢ y = y - (x + x); 其他情况下,x ♢ y = (y * x)。 和 ⊕,规则如下: 当x小于y时,x ⊕ y = y + x + y; 其他情况下,x ⊕ y = y ♢ 5 + 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: 7 ⊕ 10 ♢ 2 ♡ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "118", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ⊕ 10 ♢ 2 ♡ 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) + x. The precedence of operations: ▽ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 3 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
定义 ▽,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 = y + y / y * x * 4。 运算优先级:** = ▽ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 2 * 4 ▽ 4 + 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "47", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 * 4 ▽ 4 + 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting...
logic-v2
Define ▽, the rules are as follows: on the real number field, x ▽ y = y - y * x. The precedence of operations: ** > * = / = % > + = - = ▽。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 8 ** 3 ▽ 3 / 3 Please fill your...
{ "game_data": { "answer": "-511", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ** 3 ▽ 3 / 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nest...
logic-v2
定义 △,规则如下: 实数域上,x △ y = (x + 1) * y + 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: 6 △ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "96", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 △ 8", "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大于y时,x ♡ y = y * y - x; 其他情况下,x ♡ y = y * x ** 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: 8 ☆ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "70", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ☆ 10", "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 + 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: 1 * 5 ○ 9 / 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "1.666667", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 * 5 ○ 9 / 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 = (y * x - x)。 和 ◎,规则如下: 当y是奇数时,x ◎ y = abs(x / y); 其他情况下,x ◎ y = y * (y + x)。 运算优先级:◎ > ** > * = / = % = □ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 8 □ 6 ◎ 7 ** 4 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-3.681799", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 □ 6 ◎ 7 ** 4", "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 = x + y - 5. and ◎, the rules are as follows: when x is odd, x ◎ y = y / 5 ** x; otherwise, x ◎ y = x / y. and ⊙, the rules are as follows: when the sum of x and y is odd, x ⊙ y = x + 2 ♢ y; otherwise, x ⊙ y = x - y / y. The precedence of ope...
{ "game_data": { "answer": "-4.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ◎ 2 ♢ 2 ⊙ 5", "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 less than y, x ♡ y = x - y - y; otherwise, x ♡ y = x + abs(x + y). and ♢, the rules are as follows: on the real number field, x ♢ y = x + 5 * y. The precedence of operations: ♡ > ♢ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression ins...
{ "game_data": { "answer": "16", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ♡ 6 ♢ 3 ♢ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting...
logic-v2
定义 ◇,规则如下: 当y是偶数时,x ◇ y = 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: 3 ◇ 8 - 9 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-28", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ◇ 8 - 9", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_de...
logic-v2
定义 ☆,规则如下: 当x大于y时,x ☆ y = 3 * 5 - x - x - y; 其他情况下,x ☆ y = x * (x - 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 * y + x + x + y。 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: 4 □ 10 ♢ 1 ☆ 4 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-11", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 □ 10 ♢ 1 ☆ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesti...
logic-v2
Define ◎, the rules are as follows: when the sum of x and y is odd, x ◎ y = x * y / x * x - x; otherwise, x ◎ y = 2 * x ** y + x + y. and ♡, the rules are as follows: when x is less than y, x ♡ y = y / x / x; otherwise, x ♡ y = x + x ◎ y + x / y. and △, the rules are as follows: when x is even, x △ y = 3 + y ...
{ "game_data": { "answer": "120", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 △ 3 ◎ 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_de...
logic-v2
Define ♡, the rules are as follows: when x is a multiple of 3, x ♡ y = x * x ** y ** y + x; otherwise, x ♡ y = 1 / 5 + 5 - x * y. and ⊙, the rules are as follows: when x is even, x ⊙ y = y + 2 - x ♡ y; otherwise, x ⊙ y = y + 1 + 3 ♡ 2 * x. The precedence of operations: ** = ⊙ > * = / = % > + = - = ♡。 Parenthese...
{ "game_data": { "answer": "-165.6", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ♡ 10 ⊙ 7 * 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "ne...
logic-v2
Define ⊕, the rules are as follows: on the real number field, x ⊕ y = y - 5 + x. and ○, the rules are as follows: on the real number field, x ○ y = x * y. and ◎, the rules are as follows: when y is odd, x ◎ y = y ⊕ x ** y; otherwise, x ◎ y = y - y - x. The precedence of operations: ⊕ > ** > * = / = % > + = - = ...
{ "game_data": { "answer": "-180", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 - 2 + 8 ⊕ 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: 当x小于y时,x ♡ y = y - y / x; 其他情况下,x ♡ y = y + x * 2。 和 ⊙,规则如下: 实数域上,x ⊙ y = x ♡ 2 - y。 运算优先级:** > * = / = % = ♡ > + = - = ⊙。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 3 ⊙ 8 ♡ 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-13", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ⊙ 8 ♡ 5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_de...
logic-v2
定义 ◇,规则如下: 实数域上,x ◇ y = y - x - x。 运算优先级:** > * = / = % > + = - = ◇。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 8 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 a multiple of 5, x ⊗ y = x + y + 4; otherwise, x ⊗ y = 1 * x * y. and ⊙, the rules are as follows: on the real number field, x ⊙ y = abs(y / x) ** y. and ♡, the rules are as follows: when x is odd, x ♡ y = x + y - y; otherwise, x ♡ y = y + x. The precedence of ope...
{ "game_data": { "answer": "2.25", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ⊙ 5 * 3 * 10 ⊗ 6 ♡ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, ...
logic-v2
Define △, the rules are as follows: on the real number field, x △ y = y - y - x + 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: 5 △ 4 + 7 / 7 Please fi...
{ "game_data": { "answer": "-3", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 △ 4 + 7 / 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting...
logic-v2
定义 ⊗,规则如下: 实数域上,x ⊗ y = x - x + y - 5。 和 ⊙,规则如下: 实数域上,x ⊙ y = y - x * x * 3。 和 ◇,规则如下: 实数域上,x ◇ y = x ⊙ y + y + x * y。 运算优先级:** = ⊙ > * = / = % = ⊗ > + = - = ◇。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 8 ◇ 3 ⊗ 7 ⊙ 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-1652", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ◇ 3 ⊗ 7 ⊙ 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nest...
logic-v2
Define ▽, the rules are as follows: on the real number field, x ▽ y = x - x + 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: 5 Please fill your fina...
{ "game_data": { "answer": "5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth": null...
logic-v2
Define ○, the rules are as follows: when x and y are both even, x ○ y = x * y - y + x * 5; otherwise, x ○ y = y * y - x - x. The precedence of operations: ** > * = / = % > + = - = ○。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of t...
{ "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都是奇数时,x ◎ y = y + abs(x) * y; 其他情况下,x ◎ y = x * y - y。 和 ♢,规则如下: 实数域上,x ♢ y = x + 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: 6 ♢ 4 % 9 ◎ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "7.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ♢ 4 % 9 ◎ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nestin...
logic-v2
定义 ☆,规则如下: 实数域上,x ☆ y = 4 - y + y + x。 和 ♢,规则如下: 当x是偶数时,x ♢ y = 1 - x - y; 其他情况下,x ♢ y = x * (x) ** y - 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: 5 * 7 ☆ 8 ♢ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "55", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 * 7 ☆ 8 ♢ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting...
logic-v2
Define ☆, the rules are as follows: when x is even, x ☆ y = y + x - y + 2; otherwise, x ☆ y = x ** y ** 4 * 3. and ⊗, the rules are as follows: on the real number field, x ⊗ y = x ☆ x + y - x. and △, the rules are as follows: on the real number field, x △ y = 1 + y + y - x. The precedence of operations: △ > ☆ >...
{ "game_data": { "answer": "0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ⊗ 7 △ 1 ☆ 4", "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 = 5 + 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 + 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: 8 □ 1 □ 7 ♡ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "230", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 □ 1 □ 7 ♡ 3", "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 equal to y, x ☆ y = y + x + x - 2; otherwise, x ☆ y = x + y + y + 2. and ⊗, the rules are as follows: when y is a multiple of 3, x ⊗ y = x - x * y + x; otherwise, x ⊗ y = 5 / y * y ☆ x. The precedence of operations: ** > * = / = % = ☆ > + = - = ⊗。 Parentheses have t...
{ "game_data": { "answer": "-91", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ☆ 1 % 2 ** 9 ⊗ 9", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "n...
logic-v2
Define ⊕, the rules are as follows: when y is a multiple of 3, x ⊕ y = x + x / y; otherwise, x ⊕ y = y + y - x. 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 = x * 1 / y. The precedence of operations: ⊕ > ** > * = /...
{ "game_data": { "answer": "0.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ⊗ 6 ♢ 10 ⊕ 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 / 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 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "10", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth": nu...
logic-v2
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 = y - x / 4。 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: 2 ◇ 10 ♢ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "5.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ◇ 10 ♢ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_d...
logic-v2
定义 ○,规则如下: 当y是偶数时,x ○ y = y * x; 其他情况下,x ○ y = y + x + y + y。 运算优先级:** > * = / = % = ○ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 1 ○ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "22", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ○ 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 = abs(x - y + x ** 4) + 5. 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 - 10 ◇ 7 - 10 P...
{ "game_data": { "answer": "-10015", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 - 10 ◇ 7 - 10", "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小于y时,x ○ y = (y) * y * x + x - y; 其他情况下,x ○ y = y * x * 1 ** (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: 7 ○ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "14", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ○ 2", "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. and ◎, the rules are as follows: on the real number field, x ◎ y = 1 + y * x. The precedence of operations: □ > ** > * = / = % = ◎ > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated firs...
{ "game_data": { "answer": "46", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 □ 3 * 3 ◎ 9", "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3的倍数时,x ⊙ y = 3 + x - y ** 4; 其他情况下,x ⊙ y = y * (4 + y * x)。 和 ▽,规则如下: 实数域上,x ▽ y = x * y - x。 和 ⊕,规则如下: 当x和y的和是偶数时,x ⊕ y = 2 + x ⊙ x - y; 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: 5 ⊕ 5 ⊙ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "576", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ⊕ 5 ⊙ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_de...
logic-v2
定义 ☆,规则如下: 当y是3的倍数时,x ☆ y = x + y * x * x + x; 其他情况下,x ☆ y = x + 5 - y - x * 3。 和 ○,规则如下: 当y是奇数时,x ○ y = (y - x * y ☆ y / x); 其他情况下,x ○ y = x + 4 / 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 ☆ 1 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-26", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ○ 5 ☆ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_de...
logic-v2
Define ♢, the rules are as follows: on the real number field, x ♢ y = x + y - y. and ◎, the rules are as follows: on the real number field, x ◎ y = y - y * x. and ⊗, the rules are as follows: when x and y are both odd, x ⊗ y = y + x * y; otherwise, x ⊗ y = (y ♢ x + x). The precedence of operations: ** > * = / =...
{ "game_data": { "answer": "-49", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ⊗ 6 ◎ 7 ♢ 1", "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 = abs(x * y + y + y / x). and ▽, the rules are as follows: on the real number field, x ▽ y = x + y. and ♢, the rules are as follows: on the real number field, x ♢ y = (y - x ▽ y - y) * y. The precedence of operations: ▽ > ** > * = / = % = ⊕ = ♢ >...
{ "game_data": { "answer": "-562", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ▽ 1 ⊕ 9 ♢ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesti...
logic-v2
定义 ◇,规则如下: 当x和y的和是偶数时,x ◇ y = 2 / x - y + 2 + 4; 其他情况下,x ◇ y = y - 4 * x。 运算优先级:** = ◇ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 7 ◇ 8 * 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-140", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ◇ 8 * 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_d...
logic-v2
定义 ▽,规则如下: 实数域上,x ▽ y = abs(y - x) - y。 运算优先级:▽ > ** > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 2 % 1 ▽ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 % 1 ▽ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_dept...
logic-v2
Define □, the rules are as follows: on the real number field, x □ y = y - x - y. and ◎, the rules are as follows: when y is a multiple of 5, x ◎ y = y □ x * y; otherwise, x ◎ y = (x + y ** 3). The precedence of operations: ** > * = / = % = ◎ > + = - = □。 Parentheses have the highest priority, and the expression i...
{ "game_data": { "answer": "-9", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 □ 8 ** 3 ◎ 5 - 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "ne...
logic-v2
定义 △,规则如下: 实数域上,x △ y = x * abs(y) / x。 运算优先级:△ > ** > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "8", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth": null...
logic-v2
Define □, the rules are as follows: when y is a multiple of 5, x □ y = y + abs(x * x - 3) - y; otherwise, x □ y = (y - x - y - x). and ◎, the rules are as follows: when the sum of x and y is even, x ◎ y = (1 + y + x) + y; otherwise, x ◎ y = x / y □ y - x. The precedence of operations: ** = □ = ◎ > * = / = % > +...
{ "game_data": { "answer": "-31", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 □ 9 - 6 ◎ 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nestin...
logic-v2
Define ○, the rules are as follows: on the real number field, x ○ y = y + x - x - 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: 7 % 7 ○ 4 Please fill y...
{ "game_data": { "answer": "4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 % 7 ○ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_dept...
logic-v2
定义 ⊕,规则如下: 实数域上,x ⊕ y = y + x - y + x - y。 和 □,规则如下: 当x等于y时,x □ y = y * x ⊕ 3 / 2 - x; 其他情况下,x □ y = abs(y + y - y * x) * y。 和 ☆,规则如下: 实数域上,x ☆ y = x - x □ y + x * y。 运算优先级:** = ⊕ > * = / = % > + = - = □ = ☆。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 7 □ 4 ⊕ 10 ☆ 1 ** 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-18", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 □ 4 ⊕ 10 ☆ 1 ** 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "...
logic-v2
定义 ♡,规则如下: 实数域上,x ♡ y = x - y ** 3。 和 ♢,规则如下: 当x和y的和是偶数时,x ♢ y = x ♡ y - x; 其他情况下,x ♢ y = x ** y - x。 运算优先级:** > * = / = % = ♡ = ♢ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 10 ♡ 1 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "9", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ♡ 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 = 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 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4", "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 equal to y, x ○ y = abs(y * y) * x; otherwise, x ○ y = y + x. The precedence of operations: ** = ○ > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 3 ...
{ "game_data": { "answer": "-1", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ○ 4 - 1 - 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting...
logic-v2
定义 ◇,规则如下: 实数域上,x ◇ y = x * y - 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 ◇ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "24", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ◇ 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: 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 + y. The precedence of operations: ♡ > ** > * = / = % > + = - = ◇。 Parentheses have the highest priority, and the expression inside the parentheses is calculate...
{ "game_data": { "answer": "-2.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ◇ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth...
logic-v2
定义 ⊗,规则如下: 实数域上,x ⊗ y = x + y。 和 ⊙,规则如下: 实数域上,x ⊙ y = (x ⊗ y) - y。 和 ▽,规则如下: 实数域上,x ▽ y = y / abs(x)。 运算优先级:** = ⊙ > * = / = % > + = - = ⊗ = ▽。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 8 ⊙ 6 ⊗ 6 ▽ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "0.214286", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ⊙ 6 ⊗ 6 ▽ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "n...
logic-v2
定义 ☆,规则如下: 当x是偶数时,x ☆ y = y + y * x - y; 其他情况下,x ☆ y = x + 1 / y * x。 和 ♡,规则如下: 当x小于y时,x ♡ y = x + y + x - 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: 7 ☆ 2 / 4 ♡ 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "33", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ☆ 2 / 4 ♡ 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 = abs(y * 1 + y / y ** x). and ○, the rules are as follows: when the sum of x and y is even, x ○ y = x + x * x * x - y; otherwise, x ○ y = x - abs(y ** 2 + 2) * 5. The precedence of operations: ◎ > ** = ○ > * = / = % > + = -。 Parentheses have the...
{ "game_data": { "answer": "0.035215", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 / 8 ** 3 ○ 3 ◎ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, ...
logic-v2
Define ⊙, the rules are as follows: when y is odd, x ⊙ y = y - x - y; otherwise, x ⊙ y = (y ** y) + y / x. and ♡, the rules are as follows: on the real number field, x ♡ y = y - x ⊙ y. and ⊗, the rules are as follows: when x is greater than y, x ⊗ y = x + 2 * y + x; otherwise, x ⊗ y = (1 - y * y ♡ x). The pre...
{ "game_data": { "answer": "93327", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ⊙ 3 + 2 ♡ 6 ⊗ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, ...
logic-v2
Define ♢, the rules are as follows: when y is a multiple of 3, x ♢ y = x + 5 ** y; otherwise, x ♢ y = y - x * y. and ⊗, the rules are as follows: on the real number field, x ⊗ y = abs(y) / x. and ⊕, the rules are as follows: on the real number field, x ⊕ y = x + x * y. The precedence of operations: ⊗ > ** > * =...
{ "game_data": { "answer": "-0.6", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ♢ 10 ⊗ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_...
logic-v2
Define ♡, the rules are as follows: when the sum of x and y is even, x ♡ y = x / 5 * y * y; otherwise, x ♡ y = y + abs(x * x). and △, the rules are as follows: on the real number field, x △ y = y * y + x + y ♡ x. The precedence of operations: △ > ** > * = / = % = ♡ > + = -。 Parentheses have the highest priority, ...
{ "game_data": { "answer": "24.4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 △ 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和y的和是奇数时,x ♡ y = x + y * x; 其他情况下,x ♡ y = y + x - y。 和 ◎,规则如下: 实数域上,x ◎ y = y * x + 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 ◎ 5 ♡ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "45", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ◎ 5 ♡ 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和y都是奇数时,x ◎ y = 4 * y - (2) + 4 ** x; 其他情况下,x ◎ y = (y) - x ** x - y * x。 和 ◇,规则如下: 当x是奇数时,x ◇ y = y - y + x * y + y; 其他情况下,x ◇ y = 2 + 3 ◎ 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 ◎ 4 ◇ 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-182", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ◎ 4 ◇ 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 x and y are both odd, x ◇ y = y * y * abs(x); otherwise, x ◇ y = (y ** x) - y. The precedence of operations: ◇ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the ex...
{ "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
定义 ☆,规则如下: 实数域上,x ☆ y = x - x + y。 和 ◎,规则如下: 实数域上,x ◎ y = y ☆ x * 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 ☆ 8 ◎ 9 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "72", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ☆ 8 ◎ 9", "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 = y * x * y; 其他情况下,x ◎ y = y + 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: 3 ◎ 1 ◇ 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "40", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ◎ 1 ◇ 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 * 4 + x)。 和 ⊕,规则如下: 当x和y都是偶数时,x ⊕ y = y / x + x; 其他情况下,x ⊕ y = x * y * x + x。 和 ♡,规则如下: 实数域上,x ♡ y = 4 ⊕ x - x - y。 运算优先级:♡ > ** = ♢ = ⊕ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 5 ⊕ 10 ♡ 3 ♢ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-145.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ⊕ 10 ♡ 3 ♢ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "ne...
logic-v2
定义 □,规则如下: 当x大于y时,x □ y = x - y - y; 其他情况下,x □ y = y - x + y。 和 ♢,规则如下: 当x是3的倍数时,x ♢ y = y * x; 其他情况下,x ♢ y = x * x - y。 运算优先级:□ > ** > * = / = % = ♢ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 1 ♢ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-1", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ♢ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth":...
logic-v2
定义 ▽,规则如下: 当y是奇数时,x ▽ y = x - x - y * x; 其他情况下,x ▽ y = x + (y) / 4 + 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
Define ☆, the rules are as follows: on the real number field, x ☆ y = x * y + (y). and ○, the rules are as follows: on the real number field, x ○ y = x * y + x. The precedence of operations: ☆ = ○ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculate...
{ "game_data": { "answer": "4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ☆ 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3的倍数时,x ♡ y = x + y - x; 其他情况下,x ♡ y = x - x - y。 和 ☆,规则如下: 实数域上,x ☆ y = x - y ♡ y。 运算优先级:** > * = / = % = ♡ > + = - = ☆。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 6 ☆ 10 ☆ 6 ♡ 5 / 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "18.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ☆ 10 ☆ 6 ♡ 5 / 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "...