env
stringclasses
1 value
prompt
stringlengths
119
673
extra
dict
logic-v2
Define ▽, the rules are as follows: on the real number field, x ▽ y = y * y * y + 1 + 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 * 2 ▽ 3 - 1 Please fi...
{ "game_data": { "answer": "239", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 * 2 ▽ 3 - 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nestin...
logic-v2
定义 ▽,规则如下: 实数域上,x ▽ y = (y) * x * x - x。 和 ⊙,规则如下: 实数域上,x ⊙ y = y - x * x ** x。 和 □,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: 1 ▽ 3 ⊙ 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-77", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ▽ 3 ⊙ 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 = 2 * 4 + x - 4 * y。 和 ⊙,规则如下: 实数域上,x ⊙ y = (y - x - x / y * y)。 和 △,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: 1 △ 3 ⊙ 1 ▽ 3 ⊙ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "30", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 △ 3 ⊙ 1 ▽ 3 ⊙ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nes...
logic-v2
Define ♡, the rules are as follows: when y is even, x ♡ y = x * y; otherwise, x ♡ y = x * (y * x). and □, the rules are as follows: on the real number field, x □ y = (x - x * y). The precedence of operations: □ > ** = ♡ > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the pare...
{ "game_data": { "answer": "-280", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ♡ 10 ♡ 4 □ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nest...
logic-v2
Define ◎, the rules are as follows: when the sum of x and y is even, x ◎ y = 2 * y - x; otherwise, x ◎ y = x / y. and ☆, the rules are as follows: on the real number field, x ☆ y = y * x * x. The precedence of operations: ◎ > ** = ☆ > * = / = % > + = -。 Parentheses have the highest priority, and the expression in...
{ "game_data": { "answer": "32", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 ☆ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth":...
logic-v2
定义 ○,规则如下: 实数域上,x ○ y = y - (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 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 = abs(x - x / x + x) * y。 和 △,规则如下: 实数域上,x △ y = y + x / y - 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: 6 △ 1 ♡ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-3.4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 △ 1 ♡ 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_...
logic-v2
定义 ○,规则如下: 实数域上,x ○ y = y + y + x。 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: 9 / 5 ○ 10 * 4 ◇ 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "6.12", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 / 5 ○ 10 * 4 ◇ 5", "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 ** 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: ♢ > ** > * = / = % > + = - = ♡ = ◎。 Parenth...
{ "game_data": { "answer": "0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ♡ 7 ◎ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_dept...
logic-v2
Define ♢, the rules are as follows: when x is odd, x ♢ y = y * (x + x); otherwise, x ♢ y = (y - x) * x. and ♡, the rules are as follows: when x is a multiple of 5, x ♡ y = x + (y - y); otherwise, x ♡ y = x / y. and ◎, the rules are as follows: on the real number field, x ◎ y = x ♢ x - y. The precedence of ope...
{ "game_data": { "answer": "31.2", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ◎ 6 ♡ 5", "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 + 3 - x + y. and △, the rules are as follows: when y is a multiple of 3, x △ y = (y ⊕ x + 2); otherwise, x △ y = x / (y) / y + 1. and ♢, the rules are as follows: on the real number field, x ♢ y = abs(x * 4 * y). The precedence of operation...
{ "game_data": { "answer": "1.017751", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 △ 5 ⊕ 10", "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 = abs(y) * x * 5。 运算优先级:** > * = / = % > + = - = △。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 4 △ 8 ** 2 △ 1 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "6400", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 △ 8 ** 2 △ 1", "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 = y * y + x; otherwise, x ○ y = y * x / x. The precedence of operations: ** > * = / = % > + = - = ○。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression:...
{ "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: on the real number field, x ◎ y = abs(y / x * x). and ⊙, the rules are as follows: when x and y are both even, x ⊙ y = y ◎ y + x; otherwise, x ⊙ y = (y ◎ y + x). The precedence of operations: ** = ◎ > * = / = % = ⊙ > + = -。 Parentheses have the highest priority, and the express...
{ "game_data": { "answer": "9", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ◎ 7 ⊙ 2", "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 = x * y。 和 ○,规则如下: 当x和y的和是奇数时,x ○ y = y + x + x; 其他情况下,x ○ y = x + (y ⊗ x) / y ** x。 和 ▽,规则如下: 实数域上,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: 10 ⊗ 10 ○ 3 ▽ 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "1005", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ⊗ 10 ○ 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 even, x ♡ y = x + y; otherwise, x ♡ y = 4 ** abs(x) / y. and ◎, the rules are as follows: on the real number field, x ◎ y = 2 * x ♡ x + (5 - y). The precedence of operations: ♡ = ◎ > ** > * = / = % > + = -。 Parentheses have the highest priority, and t...
{ "game_data": { "answer": "10", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ◎ 9 ♡ 6", "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和y的和是奇数时,x ▽ y = y - x + y / x; 其他情况下,x ▽ y = 4 + 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 ▽ 4 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "2.333333", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ▽ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_d...
logic-v2
Define ⊙, the rules are as follows: when x is even, x ⊙ y = y + y - x; otherwise, x ⊙ y = x + y + x. and ◇, the rules are as follows: when x is less than y, x ◇ y = x ⊙ 4 ** y; otherwise, x ◇ y = (x * y). and ⊗, the rules are as follows: when the sum of x and y is odd, x ⊗ y = x + y - 5; otherwise, x ⊗ y = ...
{ "game_data": { "answer": "10", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ⊗ 9 ⊙ 4 ◇ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nestin...
logic-v2
Define ⊕, the rules are as follows: on the real number field, x ⊕ y = (x - y) / x. and ⊗, the rules are as follows: on the real number field, x ⊗ y = abs(x) / y. and ◇, the rules are as follows: when the sum of x and y is odd, x ◇ y = x ⊗ y - x; otherwise, x ◇ y = abs(y) ** 2 - x. The precedence of operations: ...
{ "game_data": { "answer": "0.918919", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ⊕ 7 ⊗ 7 ◇ 9 * 6", "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 = x - y * x; otherwise, x ⊙ y = x * x + 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 ** x * y. The precedence of operations: ⊙ = ◎ > ○ > ** > * = ...
{ "game_data": { "answer": "-63", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ⊙ 7 - 1 ◎ 10 ○ 9", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "n...
logic-v2
定义 ♢,规则如下: 实数域上,x ♢ y = x + y。 和 ○,规则如下: 当x是奇数时,x ○ y = y ** x + x; 其他情况下,x ○ y = x ♢ y。 和 △,规则如下: 当x是偶数时,x △ y = x ♢ 4 / 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: 10 ♢ 3 △ 1 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "10", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ♢ 3 △ 1", "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 = abs(y / x * y) - x * y。 和 ⊕,规则如下: 实数域上,x ⊕ y = 2 - x / y ♡ 3。 运算优先级:** > * = / = % = ♡ > + = - = ⊕。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 6 ⊕ 2 / 4 ♡ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-5.928571", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ⊕ 2 / 4 ♡ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "...
logic-v2
Define ▽, the rules are as follows: when y is odd, x ▽ y = (x ** x) + x - y; otherwise, x ▽ y = y * x * x + 4. The precedence of operations: ** > * = / = % = ▽ > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression:...
{ "game_data": { "answer": "154", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ▽ 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_depth"...
logic-v2
定义 ◎,规则如下: 实数域上,x ◎ y = x / x * y。 和 ♡,规则如下: 当x是5的倍数时,x ♡ y = x ◎ 1 + y; 其他情况下,x ♡ y = x + y。 运算优先级:** = ◎ > * = / = % > + = - = ♡。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 10 ♡ 1 ◎ 9 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "19", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ♡ 1 ◎ 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: 实数域上,x ♢ y = 5 - x / y。 和 ☆,规则如下: 实数域上,x ☆ y = y - y + (x)。 和 ⊗,规则如下: 当y是5的倍数时,x ⊗ y = 3 + x * y; 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: 10 ⊗ 5 ♢ 3 ☆ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-12.666667", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ⊗ 5 ♢ 3 ☆ 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 - (x * y) - y。 和 ♢,规则如下: 当y是奇数时,x ♢ y = y * abs(2 - x); 其他情况下,x ♢ y = x + x + y。 和 ◎,规则如下: 实数域上,x ◎ y = 2 / 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 ◎ 10 ♢ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "3.4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ◎ 10 ♢ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_...
logic-v2
Define ◇, the rules are as follows: when y is odd, x ◇ y = x - (y) * x + x + y; otherwise, x ◇ y = y - y * x - y * x. The precedence of operations: ** = ◇ > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expr...
{ "game_data": { "answer": "-63.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ** 2 ◇ 4 / 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nes...
logic-v2
定义 ☆,规则如下: 实数域上,x ☆ y = y + x / y。 和 ⊕,规则如下: 当x和y的和是偶数时,x ⊕ y = x - x + y; 其他情况下,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: 7 * 10 ☆ 2 ⊕ 4 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 * 10 ☆ 2 ⊕ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nestin...
logic-v2
Define △, the rules are as follows: on the real number field, x △ y = y + y + x. The precedence of operations: △ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 9 △ 5 Please fill your final an...
{ "game_data": { "answer": "19", "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
定义 ◎,规则如下: 当y是奇数时,x ◎ y = (x * x + y); 其他情况下,x ◎ y = x + 1 / 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: 4 ◎ 7 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "23", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 ◎ 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: when y is odd, x ◎ y = x + y - x; otherwise, x ◎ y = x * 5 + y. and ⊙, the rules are as follows: on the real number field, x ⊙ y = y * x ◎ x. The precedence of operations: ⊙ > ** > * = / = % > + = - = ◎。 Parentheses have the highest priority, and the expression inside the paren...
{ "game_data": { "answer": "3", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ⊙ 4 ◎ 3 % 2 ** 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nes...
logic-v2
Define ○, the rules are as follows: when x is less than y, x ○ y = (x + x + x + x) + y; otherwise, x ○ y = (y - x + x + 5 * y). The precedence of operations: ○ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value o...
{ "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 x is a multiple of 3, x ⊗ y = x - y + y - x / y; otherwise, x ⊗ y = y + x / y + y + y. and □, the rules are as follows: when x is less than y, x □ y = x + x + y - x + y; otherwise, x □ y = x - y - x + x - y. and ◇, the rules are as follows: when x is less than y, x ◇ y =...
{ "game_data": { "answer": "350", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 □ 8 ⊗ 4 ◇ 5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nestin...
logic-v2
定义 ☆,规则如下: 当y是5的倍数时,x ☆ y = (x + x / y); 其他情况下,x ☆ y = y * x + x * x。 和 ◎,规则如下: 当x是5的倍数时,x ◎ y = y - y + x * 2; 其他情况下,x ◎ y = 1 - 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 ◎ 9 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-57", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ◎ 9", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth"...
logic-v2
Define ♢, the rules are as follows: on the real number field, x ♢ y = x * y. and ☆, the rules are as follows: when x and y are both odd, x ☆ y = x / abs(y) - x; otherwise, x ☆ y = x / y ♢ y. and ◎, the rules are as follows: on the real number field, x ◎ y = y * x. The precedence of operations: ** = ☆ > * = / = ...
{ "game_data": { "answer": "-24", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ☆ 5 ♢ 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_d...
logic-v2
Define □, the rules are as follows: on the real number field, x □ y = x * y. and ☆, the rules are as follows: when x is odd, x ☆ y = abs(y + x); otherwise, x ☆ y = (x) - y + x. The precedence of operations: □ > ** = ☆ > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parent...
{ "game_data": { "answer": "-8.571429", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ☆ 8 □ 10 / 7", "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 = 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: 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和y都是偶数时,x ♢ y = x ** y; 其他情况下,x ♢ y = x - y - y。 和 ◎,规则如下: 当y是偶数时,x ◎ y = x * x / y; 其他情况下,x ◎ y = y + (y - x)。 和 ☆,规则如下: 实数域上,x ☆ y = 2 - 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: 1 ☆ 8 ♢ 6 ◎ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-43", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ☆ 8 ♢ 6 ◎ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nestin...
logic-v2
定义 ☆,规则如下: 当y是偶数时,x ☆ y = x / y + abs(x - x); 其他情况下,x ☆ y = x * 4 * y * 5 / 5。 和 ⊗,规则如下: 当y是偶数时,x ⊗ y = x ☆ (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: 1 ☆ 2 ⊗ 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-2", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ☆ 2 ⊗ 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: when x and y are both odd, x ○ y = y - y * x + x; otherwise, x ○ y = 1 + x - x * y. The precedence of operations: ** > * = / = % > + = - = ○。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the ex...
{ "game_data": { "answer": "-65534", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ○ 4 ** 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nestin...
logic-v2
定义 ◇,规则如下: 当x和y都是偶数时,x ◇ y = x - x ** y - 1; 其他情况下,x ◇ y = abs(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: 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: on the real number field, x ⊙ y = (5 - 1 - x - 3) / y. and □, the rules are as follows: when x is greater than y, x □ y = x * 4 * x * y ⊙ y; otherwise, x □ y = 4 + 4 * x * y + 3. and ☆, the rules are as follows: on the real number field, x ☆ y = y / x - x + y / y. The precede...
{ "game_data": { "answer": "1.666667", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ⊙ 3 □ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesti...
logic-v2
Define ♡, the rules are as follows: when x is a multiple of 3, x ♡ y = y * x - x + y; otherwise, x ♡ y = x * y + 4. and ☆, the rules are as follows: when x is a multiple of 3, x ☆ y = x ♡ 1 - y; otherwise, x ☆ y = (x / 4 * y). The precedence of operations: ** = ♡ > * = / = % > + = - = ☆。 Parentheses have the hi...
{ "game_data": { "answer": "87.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ♡ 8 ☆ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_d...
logic-v2
定义 ⊗,规则如下: 实数域上,x ⊗ y = abs(x + y / x) * x。 和 ⊙,规则如下: 当x是5的倍数时,x ⊙ y = y - y * x - x ⊗ y; 其他情况下,x ⊙ y = y + x * y ⊗ x。 和 □,规则如下: 当y是奇数时,x □ y = y / x + x ** y - y; 其他情况下,x □ y = 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: 9 ⊙ 6 ⊗ 1 □ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-57761", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ⊙ 6 ⊗ 1 □ 3", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nes...
logic-v2
定义 ○,规则如下: 实数域上,x ○ y = abs(5 - 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 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ○ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth": ...
logic-v2
定义 ▽,规则如下: 当y是3的倍数时,x ▽ y = y - y * abs(x); 其他情况下,x ▽ y = x + y * 2。 和 ⊕,规则如下: 实数域上,x ⊕ y = abs(x) * 5 + y。 和 ⊗,规则如下: 实数域上,x ⊗ y = x ⊕ y。 运算优先级:** > * = / = % = ▽ = ⊕ > + = - = ⊗。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 4 ⊗ 1 ⊕ 9 ⊕ 3 ⊗ 5 ▽ 4 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "478", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 ⊗ 1 ⊕ 9 ⊕ 3 ⊗ 5 ▽ 4", "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 - y / y)。 和 ☆,规则如下: 当x和y的和是奇数时,x ☆ y = (x * x) - y; 其他情况下,x ☆ y = (y + x) - x * y。 运算优先级:□ = ☆ > ** > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 1 □ 9 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "8", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 □ 9", "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 a multiple of 3, x ○ y = abs(y + x / 4); otherwise, x ○ y = x + x - y. The precedence of operations: ** > * = / = % > + = - = ○。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expre...
{ "game_data": { "answer": "-6", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 % 9 ○ 10", "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 even, x △ y = x + y - x * x - x; otherwise, x △ y = 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 expressio...
{ "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: when x is greater than y, x ☆ y = y / abs(1 * x); otherwise, x ☆ y = y + x + x. and □, the rules are as follows: when the sum of x and y is odd, x □ y = x - (x) / y; otherwise, x □ y = y + y + x. The precedence of operations: ** = ☆ > * = / = % > + = - = □。 Parentheses have t...
{ "game_data": { "answer": "3.125", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ☆ 3 □ 8 - 6 + 3", "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 = abs(y / x) * 4 + 3. 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 inside the parentheses is ca...
{ "game_data": { "answer": "0.328554", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 □ 4 ♡ 3 ♡ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "n...
logic-v2
定义 ⊕,规则如下: 实数域上,x ⊕ y = x * y。 和 ⊗,规则如下: 实数域上,x ⊗ y = x ⊕ y。 和 ☆,规则如下: 当y是5的倍数时,x ☆ y = x - x + (y); 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: 5 ⊕ 4 ⊗ 6 ☆ 1 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "180", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ⊕ 4 ⊗ 6 ☆ 1", "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 and y are both odd, x △ y = y * 4 - 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...
{ "game_data": { "answer": "60", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 △ 4 * 4", "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和y都是奇数时,x ☆ y = y + 3 + x - y; 其他情况下,x ☆ y = x + y。 和 ▽,规则如下: 当x是5的倍数时,x ▽ y = y / 2 + 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: 9 ☆ 8 * 4 ▽ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "76.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9 ☆ 8 * 4 ▽ 2", "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 odd, x □ y = x + y * y + x; otherwise, x □ y = (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 expre...
{ "game_data": { "answer": "-63", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 - 3 ○ 9 ** 1 □ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "n...
logic-v2
Define ⊕, the rules are as follows: on the real number field, x ⊕ y = y / x + 3 + y - x. and ◎, the rules are as follows: when x and y are both odd, x ◎ y = 1 * x / y - 5 - 3; otherwise, x ◎ y = y + 4 + 5 / x. and ▽, the rules are as follows: on the real number field, x ▽ y = 4 * x - x + y - x. The precedence o...
{ "game_data": { "answer": "23.833333", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ◎ 6 ▽ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nest...
logic-v2
定义 ⊕,规则如下: 当x是3的倍数时,x ⊕ y = (x) * 3 * y; 其他情况下,x ⊕ y = x ** 1 * y + y * 4。 和 ◇,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 - 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 ♢ 4 ◇ 8 ⊕ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "1980", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ♢ 4 ◇ 8 ⊕ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesti...
logic-v2
定义 ◎,规则如下: 当y是3的倍数时,x ◎ y = x - 1 - x + 5 * y; 其他情况下,x ◎ y = y + y + x * x + 2。 和 ◇,规则如下: 当x是3的倍数时,x ◇ y = 2 + x - y + x ◎ y; 其他情况下,x ◇ y = x + y + y ◎ (y) - x。 和 ♢,规则如下: 实数域上,x ♢ y = 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: 2 ◎ 6 ♢ 3 ◇ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "23604", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ◎ 6 ♢ 3 ◇ 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nes...
logic-v2
Define ◇, the rules are as follows: when y is a multiple of 3, x ◇ y = x * y ** y - y; otherwise, x ◇ y = (2 + x - 5) * y. and ⊙, the rules are as follows: on the real number field, x ⊙ y = abs(x * y). and ⊕, the rules are as follows: on the real number field, x ⊕ y = x / x + y ◇ x. The precedence of operations...
{ "game_data": { "answer": "0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ◇ 2 ⊙ 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_dep...
logic-v2
Define ♢, the rules are as follows: on the real number field, x ♢ y = x - y * y * y + y. and ◎, the rules are as follows: on the real number field, x ◎ y = y + (4) + x * x - x. and ⊕, the rules are as follows: on the real number field, x ⊕ y = (y) - y + y ◎ y - x. The precedence of operations: ◎ = ⊕ > ** > * = / ...
{ "game_data": { "answer": "13", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ◎ 9 ♢ 7 ⊕ 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3的倍数时,x ☆ y = y / x - y / y - 4; 其他情况下,x ☆ y = y - y / y - x + x。 和 △,规则如下: 实数域上,x △ y = 3 / y * 3 - x + y。 运算优先级:** > * = / = % > + = - = ☆ = △。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 6 ☆ 9 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-3.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "6 ☆ 9", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth...
logic-v2
定义 ⊗,规则如下: 当x和y的和是偶数时,x ⊗ y = x ** y - x; 其他情况下,x ⊗ y = y - x * y - y。 和 ⊙,规则如下: 实数域上,x ⊙ y = x - x / 1 + 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 ⊗ 3 ⊙ 10 ⊕ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-630", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ⊗ 3 ⊙ 10 ⊕ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nest...
logic-v2
定义 △,规则如下: 当x大于y时,x △ y = (y + x); 其他情况下,x △ y = 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: 1 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "1", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_depth": null...
logic-v2
定义 ⊗,规则如下: 实数域上,x ⊗ y = 3 * y - (5 * x) + y。 和 ○,规则如下: 当y是奇数时,x ○ y = y + y - x; 其他情况下,x ○ y = abs(x * x * y)。 和 ◇,规则如下: 当y是偶数时,x ◇ y = (x + y ○ y) - y * x; 其他情况下,x ◇ y = (y - x) * x。 运算优先级:○ > ** = ⊗ > * = / = % > + = - = ◇。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 3 ○ 5 ⊗ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-3", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 ○ 5 ⊗ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_dep...
logic-v2
Define □, the rules are as follows: when x is a multiple of 3, x □ y = 1 + y * abs(x - x) + y; otherwise, x □ y = x + x * 4 + y. and ⊕, the rules are as follows: on the real number field, x ⊕ y = x * y □ x * y - y. and ☆, the rules are as follows: on the real number field, x ☆ y = x - y * y - y + x. The precede...
{ "game_data": { "answer": "133", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ⊕ 6 □ 5 ☆ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nestin...
logic-v2
定义 ☆,规则如下: 实数域上,x ☆ y = x + y + x + y。 和 □,规则如下: 实数域上,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: 8 □ 3 + 10 ☆ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "19.666667", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 □ 3 + 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 = abs(1 * y + x)。 和 ⊕,规则如下: 实数域上,x ⊕ y = y + abs(x + x)。 和 ◎,规则如下: 当y是5的倍数时,x ◎ y = 4 * y + y - (x); 其他情况下,x ◎ y = (y + y) - x / y。 运算优先级:** = ⊗ > * = / = % > + = - = ⊕ = ◎。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 1 ⊗ 1 ⊕ 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "10", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ⊗ 1 ⊕ 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_dep...
logic-v2
Define ♡, the rules are as follows: when x and y are both even, x ♡ y = x ** 3 - y; otherwise, x ♡ y = x + y * x. and ☆, the rules are as follows: when x is greater than y, x ☆ y = x ** y + y; otherwise, x ☆ y = y - x - x. The precedence of operations: ** = ☆ > * = / = % = ♡ > + = -。 Parentheses have the highes...
{ "game_data": { "answer": "4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ☆ 2 ♡ 5 ☆ 6", "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 - y. The precedence of operations: ** > * = / = % > + = - = ○。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 7 Please fill your final an...
{ "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
Define ○, the rules are as follows: when x and y are both even, x ○ y = y + y - x + y + x; otherwise, x ○ y = y * 1 - x ** y + 1. The precedence of operations: ○ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value...
{ "game_data": { "answer": "50", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 * 1 ○ 10", "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 * y - y * y - y; otherwise, x ⊙ y = x / y ** x. and ☆, the rules are as follows: when x and y are both even, x ☆ y = x ⊙ y * 3 - y * x; otherwise, x ☆ y = y + 4 - 2 * x. and ⊗, the rules are as follows: when x is equal to y, x ⊗ y = x * ...
{ "game_data": { "answer": "-1811", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ⊗ 7 ☆ 10 ⊙ 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "ne...
logic-v2
定义 ○,规则如下: 当y是偶数时,x ○ y = y + x * y; 其他情况下,x ○ y = x + (x ** y) - 5。 运算优先级:** > * = / = % > + = - = ○。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 5 ○ 2 ○ 10 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "130", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ○ 2 ○ 10", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_d...
logic-v2
Define ○, the rules are as follows: on the real number field, x ○ y = y + x * 2 + y. The precedence of operations: ** > * = / = % = ○ > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 7 ○ 1 * 3 Please fill your ...
{ "game_data": { "answer": "48", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ○ 1 * 3", "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 * x。 和 ○,规则如下: 当x和y都是奇数时,x ○ y = y + x; 其他情况下,x ○ y = x * abs(y)。 运算优先级:○ > ** > * = / = % > + = - = ◎。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 7 ○ 3 + 8 ◎ 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "90", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ○ 3 + 8 ◎ 5", "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) * x. and ◎, the rules are as follows: when x is even, x ◎ y = x + x - y; otherwise, x ◎ y = (x □ y + y). The precedence of operations: ** > * = / = % = □ = ◎ > + = -。 Parentheses have the highest priority, and the expression inside the p...
{ "game_data": { "answer": "288", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "5 ◎ 6 □ 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: on the real number field, x △ y = x - 5 + x / y. The precedence of operations: ** > * = / = % = △ > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 4 △ 5 Please fill your fina...
{ "game_data": { "answer": "-0.2", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 △ 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 * x - x * x. and ▽, the rules are as follows: on the real number field, x ▽ y = (y + x) - 2 - x + 1. and ⊙, the rules are as follows: on the real number field, x ⊙ y = y + y ⊗ 4 - x * 4. The precedence of operations: ⊙ > ** = ⊗ > * = / = % = ...
{ "game_data": { "answer": "-133", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ⊗ 4 ⊙ 4", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_d...
logic-v2
定义 ◇,规则如下: 实数域上,x ◇ y = 3 - 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 ◇ 3 ◇ 3 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "2194", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ◇ 3 ◇ 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 = y - x + 4 + x. and ▽, the rules are as follows: when x is a multiple of 5, x ▽ y = x * abs(x + y); otherwise, x ▽ y = y * (x + x ** y). The precedence of operations: ▽ > ** > * = / = % > + = - = ◎。 Parentheses have the highest priority, and the...
{ "game_data": { "answer": "13", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "8 ◎ 9", "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 = abs(x + x * x) + y. The precedence of operations: ** = △ > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is calculated first. Please calculate the value of the expression: 3 - 1 - 9 △ 5 Please f...
{ "game_data": { "answer": "-93", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "3 - 1 - 9 △ 5", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nestin...
logic-v2
定义 ♡,规则如下: 实数域上,x ♡ y = y / (y - x * x) * y。 和 ○,规则如下: 当x和y的和是偶数时,x ○ y = (x ** y ** y); 其他情况下,x ○ y = x * x + x ♡ x - y。 运算优先级:○ > ** = ♡ > * = / = % > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 10 ○ 9 ♡ 1 ** 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "0.0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ○ 9 ♡ 1 ** 8", "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 + y * y + x. and ◇, the rules are as follows: when x is a multiple of 5, x ◇ y = y - y ○ x; otherwise, x ◇ y = x + y - x + 5. and ◎, the rules are as follows: when x is less than y, x ◎ y = y * x + y + x + y; otherwise, x ◎ y = x + y....
{ "game_data": { "answer": "2", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 % 8 ** 1 ◎ 9 ○ 6 ◇ 7", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, ...
logic-v2
Define ☆, the rules are as follows: when x is a multiple of 3, x ☆ y = x + y - y * y; otherwise, x ☆ y = y - 3 + x * y * x. and ♢, the rules are as follows: when y is a multiple of 5, x ♢ y = 5 + y + y / y ☆ x; otherwise, x ♢ y = x + (y * y * y) - x. The precedence of operations: ☆ > ** > * = / = % = ♢ > + = -。...
{ "game_data": { "answer": "1", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "7 ☆ 9 ♢ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "english", "n_types": null, "nesting_dept...
logic-v2
Define ☆, the rules are as follows: when the sum of x and y is odd, x ☆ y = (x + x) + y + x + y; otherwise, x ☆ y = x / x * y + x + x. and ⊗, the rules are as follows: when the sum of x and y is odd, x ⊗ y = x - y * x - x ☆ y; otherwise, x ⊗ y = y * y ☆ 4 * x + 4. The precedence of operations: ☆ > ⊗ > ** > * = ...
{ "game_data": { "answer": "0", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ⊗ 7 ☆ 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: 实数域上,x ☆ y = y * y + x * 1。 和 ◇,规则如下: 当x和y的和是偶数时,x ◇ y = (x * x ☆ y * x); 其他情况下,x ◇ y = (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: 10 ◇ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "7400", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ◇ 8", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_dept...
logic-v2
定义 ⊕,规则如下: 实数域上,x ⊕ y = 2 * y * x。 和 △,规则如下: 实数域上,x △ y = y ⊕ x - x * (x)。 和 ◇,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 ⊕ 2 △ 1 △ 9 % 3 ◇ 8 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "32", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 ⊕ 2 △ 1 △ 9 % 3 ◇ 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 + y * x。 运算优先级:** > * = / = % = ◇ > + = -。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 1 ◇ 5 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "6", "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
Define ☆, the rules are as follows: on the real number field, x ☆ y = x * y. and ⊗, the rules are as follows: when x is greater than y, x ⊗ y = y * y - x ☆ y; otherwise, x ⊗ y = (y + x). The precedence of operations: ☆ > ** > * = / = % = ⊗ > + = -。 Parentheses have the highest priority, and the expression inside ...
{ "game_data": { "answer": "-127", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 ☆ 7 ⊗ 6 ⊗ 5", "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 = 1 - y * x + y. and ⊗, the rules are as follows: when x is odd, x ⊗ y = y * y + x - y; otherwise, x ⊗ y = 4 ◎ y / x. The precedence of operations: ◎ > ⊗ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside t...
{ "game_data": { "answer": "0.4", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "2 ⊗ 2 ⊗ 4 % 1 ◎ 3", "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 * y - x * (y * x). and ◇, the rules are as follows: on the real number field, x ◇ y = y - y * y / y * x. and □, the rules are as follows: when x is equal to y, x □ y = y + y - (x * y); otherwise, x □ y = x / y * x + 1 + 4. The precedence of...
{ "game_data": { "answer": "-31.5", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 □ 2 ◇ 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 * y + y + y. and ⊗, the rules are as follows: on the real number field, x ⊗ y = x * y - x + y. The precedence of operations: ⊗ > ♡ > ** > * = / = % > + = -。 Parentheses have the highest priority, and the expression inside the parentheses is cal...
{ "game_data": { "answer": "432", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ♡ 9 * 2 ⊗ 2", "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 greater than y, x ○ y = x * x + x - y; otherwise, x ○ y = 1 / 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 e...
{ "game_data": { "answer": "9", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "9", "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(y) * x + x。 和 ♢,规则如下: 当x是3的倍数时,x ♢ y = y * 3 + x / x * 3; 其他情况下,x ♢ y = y + x + y + y + y。 运算优先级:** > * = / = % = ♢ > + = - = ♡。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 10 ♢ 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "34", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ♢ 6", "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等于y时,x ♡ y = y - x + y * 1; 其他情况下,x ♡ y = y - y + x。 和 ⊗,规则如下: 当x和y的和是偶数时,x ⊗ y = x * 4 * y; 其他情况下,x ⊗ y = y - x - y * 3。 运算优先级:** = ♡ > * = / = % > + = - = ⊗。 括号具有最高优先级,先计算括号内的表达式。 请计算表达式的值: 2 ⊗ 5 ♡ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-12", "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_de...
logic-v2
Define ♢, the rules are as follows: when the sum of x and y is odd, x ♢ y = y + y - y * x; otherwise, x ♢ y = x * x * y * x. and ⊗, the rules are as follows: when x is greater than y, x ⊗ y = 5 + 1 + x / y; otherwise, x ⊗ y = y + y - x + y. and ▽, the rules are as follows: on the real number field, x ▽ y = 5 ...
{ "game_data": { "answer": "-768", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 ♢ 5 ▽ 2", "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y是偶数时,x ◎ y = y / (y) * x; 其他情况下,x ◎ y = 3 - x / 4 + y。 和 □,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: 1 / 10 □ 1 ◎ 5 □ 1 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "2.25", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "1 / 10 □ 1 ◎ 5 □ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "...
logic-v2
定义 ▽,规则如下: 当y是奇数时,x ▽ y = y * 3 - 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: 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 - x - x / y。 和 △,规则如下: 当x和y的和是偶数时,x △ y = x / y + 1 / x; 其他情况下,x △ y = 2 * 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 ♡ 6 ♡ 4 △ 2 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-4.8", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 ♡ 6 ♡ 4 △ 2", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nest...
logic-v2
定义 □,规则如下: 实数域上,x □ y = y + y + x。 和 △,规则如下: 实数域上,x △ y = x - y - y * y - y。 和 ♢,规则如下: 实数域上,x ♢ y = (y △ 5 / 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: 10 □ 7 ♢ 7 △ 1 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "-5.291667", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "10 □ 7 ♢ 7 △ 1", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, ...
logic-v2
定义 ◇,规则如下: 当x是3的倍数时,x ◇ y = abs(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: 4 % 7 ◇ 6 请将最终答案填入\boxed{}中。
{ "game_data": { "answer": "6", "difficulty": 1, "gpt_response": "", "metadata": { "closing_sequence": null, "expression": "4 % 7 ◇ 6", "fill_length": null, "full_sequence": null, "is_solvable": null, "language": "chinese", "n_types": null, "nesting_dept...