task_id stringlengths 23 52 | subset stringclasses 1
value | family stringclasses 80
values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-rg-graph-color-l2-s6 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 2 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 6], [1, 4], [1, 5], [1, 9], [2, 8], [2, 9], [4, 5], [4, 6], [4, 7], [5, 6], [6, 7], [7, 8]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_9]} whe... | {"num_vertices": 10, "num_colors": 4, "edges": [[0, 6], [1, 4], [1, 5], [1, 9], [2, 8], [2, 9], [4, 5], [4, 6], [4, 7], [5, 6], [6, 7], [7, 8]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 1, 1, 2, 3, 4, 1, 2, 2]} | 1 |
construct-rg-graph-color-l2-s7 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 2 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 4], [0, 7], [3, 8], [3, 9], [4, 5], [4, 6], [6, 9]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c_9]} where c_i in 1..4 is the colour of vertex i... | {"num_vertices": 10, "num_colors": 4, "edges": [[0, 4], [0, 7], [3, 8], [3, 9], [4, 5], [4, 6], [6, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 1, 1, 2, 1, 1, 2, 2, 2]} | 1 |
construct-rg-graph-color-l2-s8 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 2 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 1], [0, 2], [0, 4], [0, 6], [1, 2], [1, 6], [1, 9], [2, 7], [3, 4], [3, 6], [3, 7], [4, 6], [6, 7], [6, 9]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1... | {"num_vertices": 10, "num_colors": 4, "edges": [[0, 1], [0, 2], [0, 4], [0, 6], [1, 2], [1, 6], [1, 9], [2, 7], [3, 4], [3, 6], [3, 7], [4, 6], [6, 7], [6, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 2, 3, 1, 2, 1, 3, 2, 1, 1]} | 1 |
construct-rg-graph-color-l2-s9 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 2 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 9], [1, 3], [1, 4], [1, 5], [1, 6], [2, 4], [2, 7], [2, 8], [2, 9], [3, 4], [4, 9], [5, 8], [6, 9]]
Possible colours: [1, 2, 3, 4]
Answer format: {"coloring": [c_0, c_1, ..., c... | {"num_vertices": 10, "num_colors": 4, "edges": [[0, 9], [1, 3], [1, 4], [1, 5], [1, 6], [2, 4], [2, 7], [2, 8], [2, 9], [3, 4], [4, 9], [5, 8], [6, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 1, 2, 3, 2, 2, 2, 3, 4]} | 1 |
construct-rg-graph-color-l3-s0 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 3 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 3], [0, 5], [0, 6], [1, 3], [1, 5], [1, 9], [2, 4], [2, 5], [2, 6], [3, 6], [4, 8], [5, 6]]
Possible colours: [1, 2, 3]
Answer format: {"coloring": [c_0, c_1, ..., c_9]} where ... | {"num_vertices": 10, "num_colors": 3, "edges": [[0, 3], [0, 5], [0, 6], [1, 3], [1, 5], [1, 9], [2, 4], [2, 5], [2, 6], [3, 6], [4, 8], [5, 6]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 1, 2, 2, 2, 3, 1, 1, 2]} | 1 |
construct-rg-graph-color-l3-s1 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 3 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 5], [0, 6], [0, 8], [1, 3], [1, 7], [1, 8], [2, 5], [2, 6], [2, 7], [3, 9], [4, 5], [4, 7], [5, 6], [5, 7], [6, 8], [7, 8], [7, 9]]
Possible colours: [1, 2, 3]
Answer format: {... | {"num_vertices": 10, "num_colors": 3, "edges": [[0, 5], [0, 6], [0, 8], [1, 3], [1, 7], [1, 8], [2, 5], [2, 6], [2, 7], [3, 9], [4, 5], [4, 7], [5, 6], [5, 7], [6, 8], [7, 8], [7, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 1, 2, 1, 2, 3, 3, 2, 1]} | 1 |
construct-rg-graph-color-l3-s2 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 3 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 8], [0, 9], [1, 2], [1, 8], [2, 3], [2, 6], [2, 9], [3, 5], [3, 9], [4, 9]]
Possible colours: [1, 2, 3]
Answer format: {"coloring": [c_0, c_1, ..., c_9]} where c_i in 1..3 is t... | {"num_vertices": 10, "num_colors": 3, "edges": [[0, 8], [0, 9], [1, 2], [1, 8], [2, 3], [2, 6], [2, 9], [3, 5], [3, 9], [4, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 2, 1, 1, 2, 1, 1, 2, 3]} | 1 |
construct-rg-graph-color-l3-s3 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 3 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 1], [0, 6], [0, 8], [1, 2], [1, 5], [2, 3], [2, 4], [3, 6], [3, 9], [4, 6], [4, 7], [5, 6], [7, 8], [7, 9], [8, 9]]
Possible colours: [1, 2, 3]
Answer format: {"coloring": [c_0... | {"num_vertices": 10, "num_colors": 3, "edges": [[0, 1], [0, 6], [0, 8], [1, 2], [1, 5], [2, 3], [2, 4], [3, 6], [3, 9], [4, 6], [4, 7], [5, 6], [7, 8], [7, 9], [8, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 2, 1, 2, 2, 1, 3, 1, 2, 3]} | 1 |
construct-rg-graph-color-l3-s4 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 3 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 1], [0, 5], [0, 8], [1, 2], [1, 5], [1, 6], [1, 7], [1, 9], [2, 5], [5, 6], [5, 7], [5, 9], [7, 8]]
Possible colours: [1, 2, 3]
Answer format: {"coloring": [c_0, c_1, ..., c_9]... | {"num_vertices": 10, "num_colors": 3, "edges": [[0, 1], [0, 5], [0, 8], [1, 2], [1, 5], [1, 6], [1, 7], [1, 9], [2, 5], [5, 6], [5, 7], [5, 9], [7, 8]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 2, 1, 1, 1, 3, 1, 1, 2, 1]} | 1 |
construct-rg-graph-color-l3-s5 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 3 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 1], [0, 4], [0, 5], [0, 6], [1, 2], [1, 7], [2, 4], [2, 5], [2, 7], [2, 9], [3, 7], [3, 8], [4, 7], [5, 8], [5, 9]]
Possible colours: [1, 2, 3]
Answer format: {"coloring": [c_0... | {"num_vertices": 10, "num_colors": 3, "edges": [[0, 1], [0, 4], [0, 5], [0, 6], [1, 2], [1, 7], [2, 4], [2, 5], [2, 7], [2, 9], [3, 7], [3, 8], [4, 7], [5, 8], [5, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 2, 1, 1, 2, 2, 2, 3, 3, 3]} | 1 |
construct-rg-graph-color-l3-s6 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 3 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 5], [1, 2], [3, 5], [3, 7], [4, 5], [4, 7], [4, 8], [4, 9], [5, 6], [6, 8]]
Possible colours: [1, 2, 3]
Answer format: {"coloring": [c_0, c_1, ..., c_9]} where c_i in 1..3 is t... | {"num_vertices": 10, "num_colors": 3, "edges": [[0, 5], [1, 2], [3, 5], [3, 7], [4, 5], [4, 7], [4, 8], [4, 9], [5, 6], [6, 8]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 2, 1, 1, 2, 1, 2, 2, 2]} | 1 |
construct-rg-graph-color-l3-s7 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 3 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 3], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [2, 4], [2, 5], [2, 8], [3, 9], [4, 6], [4, 7], [4, 9], [6, 8], [7, 9]]
Possible colours: [1, 2, 3]
Answer format: {"coloring": [c_0... | {"num_vertices": 10, "num_colors": 3, "edges": [[0, 3], [1, 2], [1, 3], [1, 4], [1, 6], [1, 7], [2, 4], [2, 5], [2, 8], [3, 9], [4, 6], [4, 7], [4, 9], [6, 8], [7, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 2, 2, 3, 1, 2, 2, 1, 1]} | 1 |
construct-rg-graph-color-l3-s8 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 3 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[1, 9], [2, 6], [2, 7], [3, 5], [3, 6], [4, 7], [8, 9]]
Possible colours: [1, 2, 3]
Answer format: {"coloring": [c_0, c_1, ..., c_9]} where c_i in 1..3 is the colour of vertex i
W... | {"num_vertices": 10, "num_colors": 3, "edges": [[1, 9], [2, 6], [2, 7], [3, 5], [3, 6], [4, 7], [8, 9]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 1, 1, 1, 1, 2, 2, 2, 1, 2]} | 1 |
construct-rg-graph-color-l3-s9 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 3 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Edges: [[0, 1], [0, 3], [0, 5], [0, 6], [0, 8], [1, 4], [1, 6], [1, 8], [2, 3], [2, 5], [2, 7], [4, 5], [4, 8], [5, 7]]
Possible colours: [1, 2, 3]
Answer format: {"coloring": [c_0, c_1, .... | {"num_vertices": 10, "num_colors": 3, "edges": [[0, 1], [0, 3], [0, 5], [0, 6], [0, 8], [1, 4], [1, 6], [1, 8], [2, 3], [2, 5], [2, 7], [4, 5], [4, 8], [5, 7]], "family": "rg_graph_color", "subset": "construct"} | null | null | null | {"coloring": [1, 2, 1, 2, 1, 2, 3, 3, 3, 1]} | 1 |
construct-rg-graph-color-l4-s0 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 4 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
Edges: [[0, 7], [0, 8], [0, 11], [0, 14], [1, 2], [1, 5], [1, 9], [2, 8], [3, 7], [3, 8], [3, 12], [3, 15], [3, 16], [4, 6], [4, 8], [4, 11], [5, 6],... | {"num_vertices": 20, "num_colors": 3, "edges": [[0, 7], [0, 8], [0, 11], [0, 14], [1, 2], [1, 5], [1, 9], [2, 8], [3, 7], [3, 8], [3, 12], [3, 15], [3, 16], [4, 6], [4, 8], [4, 11], [5, 6], [5, 7], [5, 18], [6, 11], [6, 15], [7, 9], [7, 13], [7, 14], [7, 15], [7, 17], [7, 19], [8, 10], [8, 14], [9, 10], [9, 13], [10, 1... | null | null | null | {"coloring": [1, 1, 2, 1, 1, 2, 3, 3, 3, 2, 1, 2, 2, 1, 2, 2, 3, 1, 3, 2]} | 1 |
construct-rg-graph-color-l4-s1 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 4 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
Edges: [[0, 7], [0, 8], [0, 17], [0, 19], [2, 8], [3, 4], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 16], [4, 12], [4, 17], [5, 6... | {"num_vertices": 20, "num_colors": 3, "edges": [[0, 7], [0, 8], [0, 17], [0, 19], [2, 8], [3, 4], [3, 6], [3, 7], [3, 8], [3, 9], [3, 10], [3, 11], [3, 12], [3, 16], [4, 12], [4, 17], [5, 6], [5, 12], [6, 7], [6, 18], [7, 10], [8, 14], [10, 13], [10, 19], [12, 15], [13, 19], [15, 16], [17, 18]], "family": "rg_graph_col... | null | null | null | {"coloring": [1, 1, 1, 1, 2, 1, 2, 3, 2, 2, 2, 2, 3, 1, 1, 1, 2, 3, 1, 3]} | 1 |
construct-rg-graph-color-l4-s2 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 4 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
Edges: [[0, 2], [0, 4], [0, 11], [0, 18], [1, 13], [1, 19], [2, 3], [2, 6], [2, 14], [3, 15], [4, 8], [4, 19], [5, 16], [6, 11], [7, 15], [8, 16], [8... | {"num_vertices": 20, "num_colors": 3, "edges": [[0, 2], [0, 4], [0, 11], [0, 18], [1, 13], [1, 19], [2, 3], [2, 6], [2, 14], [3, 15], [4, 8], [4, 19], [5, 16], [6, 11], [7, 15], [8, 16], [8, 17], [8, 18], [9, 14], [10, 11], [10, 13], [10, 18], [11, 12], [11, 18], [12, 16], [13, 14], [13, 16], [13, 18], [13, 19], [14, 1... | null | null | null | {"coloring": [1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 3, 2, 3, 2, 3, 3]} | 1 |
construct-rg-graph-color-l4-s3 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 4 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
Edges: [[0, 9], [0, 13], [1, 16], [1, 17], [2, 5], [2, 7], [2, 13], [2, 15], [3, 8], [3, 9], [3, 13], [4, 6], [4, 9], [5, 9], [5, 10], [5, 13], [5, 1... | {"num_vertices": 20, "num_colors": 3, "edges": [[0, 9], [0, 13], [1, 16], [1, 17], [2, 5], [2, 7], [2, 13], [2, 15], [3, 8], [3, 9], [3, 13], [4, 6], [4, 9], [5, 9], [5, 10], [5, 13], [5, 19], [6, 16], [6, 18], [8, 9], [8, 16], [9, 11], [10, 15], [11, 12], [11, 15], [13, 18], [15, 17], [16, 19], [17, 18], [17, 19]], "f... | null | null | null | {"coloring": [1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 1, 1, 2, 3, 1, 2, 3, 3, 1, 1]} | 1 |
construct-rg-graph-color-l4-s4 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 4 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
Edges: [[0, 3], [0, 6], [0, 9], [0, 11], [0, 15], [0, 18], [1, 9], [1, 11], [1, 12], [1, 13], [1, 17], [1, 18], [2, 10], [2, 11], [2, 14], [2, 15], [... | {"num_vertices": 20, "num_colors": 3, "edges": [[0, 3], [0, 6], [0, 9], [0, 11], [0, 15], [0, 18], [1, 9], [1, 11], [1, 12], [1, 13], [1, 17], [1, 18], [2, 10], [2, 11], [2, 14], [2, 15], [2, 17], [2, 19], [3, 13], [4, 14], [4, 19], [5, 6], [5, 12], [5, 13], [6, 13], [6, 14], [6, 17], [7, 10], [7, 14], [7, 19], [8, 13]... | null | null | null | {"coloring": [1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 3, 3, 3, 1, 3, 3, 3]} | 1 |
construct-rg-graph-color-l4-s5 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 4 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
Edges: [[0, 4], [0, 19], [1, 4], [1, 13], [3, 9], [3, 13], [4, 5], [4, 17], [4, 19], [5, 7], [5, 9], [5, 14], [5, 15], [6, 7], [6, 15], [6, 18], [7, ... | {"num_vertices": 20, "num_colors": 3, "edges": [[0, 4], [0, 19], [1, 4], [1, 13], [3, 9], [3, 13], [4, 5], [4, 17], [4, 19], [5, 7], [5, 9], [5, 14], [5, 15], [6, 7], [6, 15], [6, 18], [7, 19], [8, 9], [8, 11], [8, 14], [8, 16], [10, 11], [10, 14], [11, 16], [12, 16], [12, 18], [14, 16], [14, 17], [15, 16], [15, 18], [... | null | null | null | {"coloring": [1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 3, 1, 3, 3]} | 1 |
construct-rg-graph-color-l4-s6 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 4 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
Edges: [[0, 1], [0, 4], [0, 7], [0, 8], [0, 16], [1, 7], [1, 17], [2, 10], [2, 13], [2, 16], [2, 17], [3, 5], [3, 8], [3, 19], [4, 17], [4, 19], [5, ... | {"num_vertices": 20, "num_colors": 3, "edges": [[0, 1], [0, 4], [0, 7], [0, 8], [0, 16], [1, 7], [1, 17], [2, 10], [2, 13], [2, 16], [2, 17], [3, 5], [3, 8], [3, 19], [4, 17], [4, 19], [5, 7], [5, 14], [5, 17], [6, 8], [7, 8], [7, 9], [7, 10], [7, 11], [8, 9], [8, 13], [8, 15], [9, 13], [9, 16], [10, 13], [10, 15], [10... | null | null | null | {"coloring": [1, 2, 1, 1, 2, 2, 1, 3, 2, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 3]} | 1 |
construct-rg-graph-color-l4-s7 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 4 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
Edges: [[0, 4], [0, 14], [0, 15], [1, 2], [1, 4], [1, 7], [2, 4], [2, 7], [2, 14], [2, 17], [2, 19], [3, 7], [3, 9], [3, 10], [3, 13], [3, 18], [4, 5... | {"num_vertices": 20, "num_colors": 3, "edges": [[0, 4], [0, 14], [0, 15], [1, 2], [1, 4], [1, 7], [2, 4], [2, 7], [2, 14], [2, 17], [2, 19], [3, 7], [3, 9], [3, 10], [3, 13], [3, 18], [4, 5], [6, 10], [6, 11], [6, 15], [7, 8], [7, 11], [8, 12], [8, 13], [8, 15], [9, 14], [10, 12], [10, 17], [12, 13], [12, 16], [12, 17]... | null | null | null | {"coloring": [1, 1, 2, 1, 3, 1, 1, 3, 1, 2, 2, 2, 3, 2, 3, 3, 1, 1, 2, 1]} | 1 |
construct-rg-graph-color-l4-s8 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 4 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
Edges: [[0, 1], [0, 3], [0, 8], [1, 3], [1, 7], [2, 6], [2, 12], [2, 13], [3, 16], [4, 6], [4, 8], [4, 16], [5, 12], [5, 13], [5, 15], [6, 19], [7, 1... | {"num_vertices": 20, "num_colors": 3, "edges": [[0, 1], [0, 3], [0, 8], [1, 3], [1, 7], [2, 6], [2, 12], [2, 13], [3, 16], [4, 6], [4, 8], [4, 16], [5, 12], [5, 13], [5, 15], [6, 19], [7, 11], [7, 16], [8, 9], [9, 10], [9, 11], [9, 18], [11, 12], [12, 14], [13, 19], [14, 15], [18, 19]], "family": "rg_graph_color", "sub... | null | null | null | {"coloring": [1, 2, 1, 3, 1, 1, 2, 1, 2, 1, 2, 2, 3, 2, 1, 2, 2, 1, 2, 1]} | 1 |
construct-rg-graph-color-l4-s9 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 4 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
Edges: [[0, 3], [0, 6], [0, 13], [0, 17], [1, 4], [2, 4], [2, 5], [2, 12], [2, 13], [2, 14], [3, 9], [4, 8], [4, 17], [4, 19], [5, 9], [5, 10], [5, 1... | {"num_vertices": 20, "num_colors": 3, "edges": [[0, 3], [0, 6], [0, 13], [0, 17], [1, 4], [2, 4], [2, 5], [2, 12], [2, 13], [2, 14], [3, 9], [4, 8], [4, 17], [4, 19], [5, 9], [5, 10], [5, 13], [5, 19], [6, 7], [7, 11], [7, 18], [8, 12], [8, 13], [10, 11], [10, 17], [11, 15], [13, 16], [14, 17], [14, 19]], "family": "rg... | null | null | null | {"coloring": [1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 3, 2, 1, 1, 3, 2, 1]} | 1 |
construct-rg-graph-color-l5-s0 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 5 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
Edges: [[0, 15], [0, 18], [0, 20], [1, 3], [1, 4], [1, 11], [1, 13], [2, 4], [2, 6], [2, 13], [2, 19], [3, 4], [3, 12], [3, 14], ... | {"num_vertices": 25, "num_colors": 3, "edges": [[0, 15], [0, 18], [0, 20], [1, 3], [1, 4], [1, 11], [1, 13], [2, 4], [2, 6], [2, 13], [2, 19], [3, 4], [3, 12], [3, 14], [3, 20], [4, 5], [4, 8], [4, 9], [4, 15], [4, 23], [5, 9], [5, 12], [5, 14], [6, 12], [6, 14], [6, 17], [7, 10], [8, 11], [8, 19], [8, 23], [9, 14], [9... | null | null | null | {"coloring": [1, 1, 1, 2, 3, 1, 2, 1, 1, 2, 2, 3, 3, 2, 3, 2, 1, 1, 3, 3, 3, 1, 1, 2, 1]} | 1 |
construct-rg-graph-color-l5-s1 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 5 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
Edges: [[0, 15], [0, 17], [0, 19], [0, 23], [1, 6], [2, 8], [2, 11], [2, 16], [2, 19], [2, 20], [2, 24], [3, 22], [3, 23], [3, 24... | {"num_vertices": 25, "num_colors": 3, "edges": [[0, 15], [0, 17], [0, 19], [0, 23], [1, 6], [2, 8], [2, 11], [2, 16], [2, 19], [2, 20], [2, 24], [3, 22], [3, 23], [3, 24], [4, 5], [4, 6], [4, 21], [5, 9], [5, 14], [5, 19], [6, 10], [6, 16], [6, 20], [7, 10], [7, 11], [7, 18], [7, 22], [8, 19], [9, 10], [10, 14], [10, 1... | null | null | null | {"coloring": [1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 3, 2, 1, 1, 1, 2, 3, 2, 3, 3, 3, 2, 2, 2, 3]} | 1 |
construct-rg-graph-color-l5-s2 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 5 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
Edges: [[0, 2], [0, 4], [0, 13], [0, 14], [0, 15], [1, 8], [1, 9], [1, 14], [1, 15], [2, 5], [2, 11], [2, 19], [2, 24], [3, 5], [... | {"num_vertices": 25, "num_colors": 3, "edges": [[0, 2], [0, 4], [0, 13], [0, 14], [0, 15], [1, 8], [1, 9], [1, 14], [1, 15], [2, 5], [2, 11], [2, 19], [2, 24], [3, 5], [3, 10], [3, 14], [3, 16], [3, 21], [4, 7], [4, 10], [4, 13], [5, 15], [5, 18], [6, 8], [6, 10], [6, 22], [6, 23], [7, 8], [7, 15], [7, 20], [8, 12], [8... | null | null | null | {"coloring": [1, 1, 2, 1, 2, 3, 1, 1, 2, 2, 3, 1, 3, 3, 2, 2, 3, 2, 1, 3, 2, 2, 3, 3, 1]} | 1 |
construct-rg-graph-color-l5-s3 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 5 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
Edges: [[0, 4], [0, 14], [1, 14], [1, 15], [1, 17], [1, 21], [1, 24], [2, 5], [2, 11], [2, 12], [2, 14], [2, 24], [3, 9], [3, 11]... | {"num_vertices": 25, "num_colors": 3, "edges": [[0, 4], [0, 14], [1, 14], [1, 15], [1, 17], [1, 21], [1, 24], [2, 5], [2, 11], [2, 12], [2, 14], [2, 24], [3, 9], [3, 11], [4, 6], [4, 8], [4, 18], [5, 6], [6, 13], [6, 14], [7, 13], [7, 16], [7, 23], [9, 13], [10, 14], [10, 15], [10, 18], [10, 24], [11, 23], [13, 22], [1... | null | null | null | {"coloring": [1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 3, 2, 2, 2, 2, 3, 1, 1, 3, 1, 3, 2]} | 1 |
construct-rg-graph-color-l5-s4 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 5 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
Edges: [[0, 2], [0, 7], [0, 9], [0, 14], [0, 19], [0, 23], [1, 15], [1, 24], [2, 5], [2, 9], [2, 16], [2, 18], [3, 6], [3, 8], [3... | {"num_vertices": 25, "num_colors": 3, "edges": [[0, 2], [0, 7], [0, 9], [0, 14], [0, 19], [0, 23], [1, 15], [1, 24], [2, 5], [2, 9], [2, 16], [2, 18], [3, 6], [3, 8], [3, 11], [3, 15], [4, 20], [4, 24], [5, 11], [5, 19], [5, 23], [7, 10], [7, 12], [7, 15], [8, 16], [8, 23], [9, 11], [9, 13], [9, 21], [10, 16], [10, 18]... | null | null | null | {"coloring": [1, 1, 2, 1, 1, 1, 2, 2, 2, 3, 1, 2, 1, 1, 2, 3, 3, 1, 3, 2, 3, 1, 1, 3, 3]} | 1 |
construct-rg-graph-color-l5-s5 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 5 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
Edges: [[0, 1], [0, 7], [0, 21], [1, 21], [2, 7], [2, 8], [2, 20], [3, 6], [3, 18], [4, 6], [4, 7], [4, 12], [5, 7], [5, 10], [5,... | {"num_vertices": 25, "num_colors": 3, "edges": [[0, 1], [0, 7], [0, 21], [1, 21], [2, 7], [2, 8], [2, 20], [3, 6], [3, 18], [4, 6], [4, 7], [4, 12], [5, 7], [5, 10], [5, 15], [5, 20], [5, 21], [6, 10], [6, 14], [6, 20], [7, 14], [7, 16], [7, 18], [8, 16], [8, 20], [9, 14], [9, 15], [9, 16], [10, 17], [12, 16], [13, 16]... | null | null | null | {"coloring": [1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 3, 1, 2, 1, 3, 2, 3, 2, 3, 1, 3, 3, 1, 2, 1]} | 1 |
construct-rg-graph-color-l5-s6 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 5 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
Edges: [[0, 1], [0, 7], [0, 10], [0, 15], [1, 5], [1, 13], [1, 14], [1, 15], [1, 19], [1, 20], [2, 5], [2, 6], [2, 11], [3, 9], [... | {"num_vertices": 25, "num_colors": 3, "edges": [[0, 1], [0, 7], [0, 10], [0, 15], [1, 5], [1, 13], [1, 14], [1, 15], [1, 19], [1, 20], [2, 5], [2, 6], [2, 11], [3, 9], [3, 11], [4, 5], [4, 16], [4, 18], [5, 23], [5, 24], [6, 22], [7, 13], [7, 17], [7, 21], [7, 24], [8, 13], [8, 16], [10, 12], [10, 13], [11, 19], [12, 1... | null | null | null | {"coloring": [1, 2, 1, 1, 1, 3, 2, 2, 1, 2, 2, 2, 1, 3, 1, 3, 2, 1, 2, 3, 3, 1, 3, 1, 1]} | 1 |
construct-rg-graph-color-l5-s7 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 5 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
Edges: [[0, 13], [0, 21], [1, 9], [1, 12], [1, 20], [1, 21], [1, 23], [2, 7], [2, 19], [3, 13], [3, 18], [4, 6], [4, 17], [4, 21]... | {"num_vertices": 25, "num_colors": 3, "edges": [[0, 13], [0, 21], [1, 9], [1, 12], [1, 20], [1, 21], [1, 23], [2, 7], [2, 19], [3, 13], [3, 18], [4, 6], [4, 17], [4, 21], [5, 20], [5, 21], [5, 23], [6, 14], [6, 21], [6, 24], [7, 10], [7, 11], [7, 13], [7, 17], [8, 10], [8, 21], [8, 23], [10, 11], [10, 15], [10, 20], [1... | null | null | null | {"coloring": [1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 3, 3, 2, 2, 3, 1, 2, 1]} | 1 |
construct-rg-graph-color-l5-s8 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 5 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
Edges: [[0, 2], [0, 10], [1, 6], [1, 11], [1, 12], [1, 20], [2, 3], [2, 5], [2, 21], [2, 24], [3, 14], [3, 17], [3, 19], [3, 21],... | {"num_vertices": 25, "num_colors": 3, "edges": [[0, 2], [0, 10], [1, 6], [1, 11], [1, 12], [1, 20], [2, 3], [2, 5], [2, 21], [2, 24], [3, 14], [3, 17], [3, 19], [3, 21], [3, 22], [4, 11], [4, 13], [4, 16], [5, 10], [5, 15], [6, 13], [6, 22], [7, 9], [8, 10], [8, 19], [9, 10], [9, 19], [10, 14], [10, 15], [10, 23], [11,... | null | null | null | {"coloring": [1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 2, 2, 3, 2, 2, 2, 3, 1, 3, 2, 3, 3, 1, 1]} | 1 |
construct-rg-graph-color-l5-s9 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 5 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]
Edges: [[0, 8], [0, 11], [0, 18], [0, 20], [1, 7], [1, 23], [2, 5], [2, 12], [2, 18], [3, 5], [4, 21], [5, 6], [5, 10], [5, 21], ... | {"num_vertices": 25, "num_colors": 3, "edges": [[0, 8], [0, 11], [0, 18], [0, 20], [1, 7], [1, 23], [2, 5], [2, 12], [2, 18], [3, 5], [4, 21], [5, 6], [5, 10], [5, 21], [5, 24], [6, 14], [6, 19], [6, 21], [7, 9], [7, 10], [7, 16], [8, 10], [8, 23], [9, 18], [9, 21], [10, 11], [10, 14], [10, 17], [10, 20], [11, 23], [11... | null | null | null | {"coloring": [1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 3, 1, 1, 2, 2, 3, 2, 3, 1, 3, 1]} | 1 |
construct-rg-graph-color-l6-s0 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 6 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
Edges: [[0, 1], [0, 11], [0, 18], [0, 33], [1, 6], [1, 15], [1, 27], ... | {"num_vertices": 40, "num_colors": 3, "edges": [[0, 1], [0, 11], [0, 18], [0, 33], [1, 6], [1, 15], [1, 27], [1, 31], [1, 37], [2, 11], [2, 26], [2, 28], [2, 31], [3, 8], [3, 11], [3, 12], [3, 14], [3, 16], [3, 32], [3, 36], [3, 38], [4, 10], [4, 20], [4, 27], [4, 32], [4, 38], [4, 39], [5, 18], [5, 31], [5, 38], [6, 9... | null | null | null | {"coloring": [1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 2, 3, 3, 1, 2, 2, 2, 2, 2, 1, 1, 3, 1, 1, 2, 3, 2, 1, 1, 3, 2, 3, 1, 2, 2, 1, 3, 3]} | 1 |
construct-rg-graph-color-l6-s1 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 6 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
Edges: [[0, 3], [0, 4], [0, 11], [0, 31], [1, 18], [1, 26], [2, 16], ... | {"num_vertices": 40, "num_colors": 3, "edges": [[0, 3], [0, 4], [0, 11], [0, 31], [1, 18], [1, 26], [2, 16], [2, 25], [3, 7], [3, 13], [3, 14], [3, 19], [3, 37], [4, 16], [4, 31], [4, 33], [4, 38], [5, 6], [5, 9], [5, 13], [5, 29], [5, 32], [5, 35], [6, 12], [6, 13], [6, 33], [6, 36], [7, 13], [7, 31], [7, 32], [7, 35]... | null | null | null | {"coloring": [1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 1, 3, 1, 2, 1, 2, 1, 2, 3, 1, 3, 2, 1, 3, 2, 2, 3, 3, 1, 1, 3, 1, 1, 3, 2]} | 1 |
construct-rg-graph-color-l6-s2 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 6 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
Edges: [[0, 1], [0, 19], [0, 30], [0, 33], [0, 34], [1, 5], [1, 15], ... | {"num_vertices": 40, "num_colors": 3, "edges": [[0, 1], [0, 19], [0, 30], [0, 33], [0, 34], [1, 5], [1, 15], [1, 18], [1, 21], [2, 9], [2, 11], [2, 20], [2, 22], [2, 28], [2, 29], [4, 17], [4, 20], [4, 29], [5, 9], [5, 17], [5, 21], [5, 32], [5, 36], [6, 18], [6, 34], [7, 10], [7, 15], [7, 24], [7, 35], [8, 9], [10, 21... | null | null | null | {"coloring": [1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 1, 2, 3, 2, 2, 3, 3, 3, 2, 1, 1, 1, 3, 2, 2, 1, 2, 2, 2, 3, 2, 2, 1, 1]} | 1 |
construct-rg-graph-color-l6-s3 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 6 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
Edges: [[0, 24], [0, 29], [0, 36], [1, 6], [1, 12], [1, 14], [1, 39],... | {"num_vertices": 40, "num_colors": 3, "edges": [[0, 24], [0, 29], [0, 36], [1, 6], [1, 12], [1, 14], [1, 39], [2, 5], [2, 14], [2, 15], [2, 21], [2, 24], [2, 34], [3, 10], [3, 11], [3, 20], [4, 7], [4, 26], [5, 23], [5, 27], [5, 29], [5, 38], [7, 8], [7, 10], [7, 23], [8, 17], [8, 24], [8, 25], [8, 35], [8, 37], [9, 10... | null | null | null | {"coloring": [1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 3, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 3, 1, 3, 3, 3, 1, 3, 3, 1, 3, 1, 3, 2, 2, 2, 2, 1, 3]} | 1 |
construct-rg-graph-color-l6-s4 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 6 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
Edges: [[0, 2], [0, 3], [0, 7], [0, 17], [1, 4], [1, 13], [1, 17], [1... | {"num_vertices": 40, "num_colors": 3, "edges": [[0, 2], [0, 3], [0, 7], [0, 17], [1, 4], [1, 13], [1, 17], [1, 26], [2, 4], [2, 7], [2, 32], [3, 8], [3, 9], [3, 15], [3, 18], [3, 28], [4, 9], [4, 13], [4, 17], [5, 11], [5, 25], [5, 30], [6, 19], [6, 22], [6, 26], [6, 30], [6, 33], [7, 10], [7, 15], [7, 18], [7, 20], [7... | null | null | null | {"coloring": [1, 1, 2, 2, 3, 1, 1, 3, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 3, 3, 2, 2, 2, 3, 1, 3, 2, 3, 1, 3, 3, 3, 3, 1, 1, 1]} | 1 |
construct-rg-graph-color-l6-s5 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 6 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
Edges: [[0, 6], [0, 12], [0, 18], [1, 10], [1, 19], [1, 20], [1, 27],... | {"num_vertices": 40, "num_colors": 3, "edges": [[0, 6], [0, 12], [0, 18], [1, 10], [1, 19], [1, 20], [1, 27], [1, 39], [2, 14], [2, 23], [2, 30], [2, 35], [3, 5], [3, 8], [3, 30], [4, 5], [4, 18], [4, 24], [4, 30], [4, 38], [5, 24], [6, 7], [6, 11], [6, 16], [6, 26], [7, 19], [7, 20], [8, 24], [9, 23], [9, 35], [9, 39]... | null | null | null | {"coloring": [1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 3, 3, 2, 1, 2, 1, 1, 2, 3, 1, 2, 2, 3, 1, 2, 3, 3]} | 1 |
construct-rg-graph-color-l6-s6 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 6 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
Edges: [[0, 6], [0, 7], [0, 10], [0, 15], [0, 33], [0, 34], [0, 38], ... | {"num_vertices": 40, "num_colors": 3, "edges": [[0, 6], [0, 7], [0, 10], [0, 15], [0, 33], [0, 34], [0, 38], [1, 11], [1, 17], [1, 31], [2, 18], [2, 27], [2, 36], [3, 15], [3, 28], [4, 9], [4, 10], [4, 14], [4, 16], [4, 21], [4, 38], [5, 6], [5, 11], [5, 13], [5, 15], [5, 16], [5, 27], [5, 28], [5, 38], [6, 29], [6, 30... | null | null | null | {"coloring": [1, 1, 1, 1, 1, 1, 2, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 3, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 2, 3, 1, 2, 1, 3, 1]} | 1 |
construct-rg-graph-color-l6-s7 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 6 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
Edges: [[0, 4], [0, 5], [0, 7], [0, 10], [0, 18], [0, 23], [0, 31], [... | {"num_vertices": 40, "num_colors": 3, "edges": [[0, 4], [0, 5], [0, 7], [0, 10], [0, 18], [0, 23], [0, 31], [1, 39], [2, 18], [2, 37], [3, 14], [3, 22], [3, 25], [3, 32], [4, 23], [4, 25], [4, 28], [4, 35], [4, 36], [4, 37], [4, 39], [5, 7], [6, 16], [6, 30], [6, 36], [6, 38], [7, 12], [7, 18], [7, 19], [7, 21], [7, 22... | null | null | null | {"coloring": [1, 1, 1, 1, 2, 2, 1, 3, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 3, 2, 3, 1, 3, 3, 1, 3, 2, 2, 1, 1, 1, 3, 3, 2, 3]} | 1 |
construct-rg-graph-color-l6-s8 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 6 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
Edges: [[0, 5], [0, 19], [0, 23], [0, 29], [0, 31], [2, 8], [2, 11], ... | {"num_vertices": 40, "num_colors": 3, "edges": [[0, 5], [0, 19], [0, 23], [0, 29], [0, 31], [2, 8], [2, 11], [2, 15], [2, 31], [2, 34], [3, 8], [3, 19], [4, 7], [4, 9], [4, 10], [4, 28], [4, 29], [5, 25], [5, 26], [5, 32], [5, 35], [6, 10], [6, 19], [6, 29], [6, 31], [7, 17], [7, 25], [7, 33], [7, 35], [7, 39], [8, 13]... | null | null | null | {"coloring": [1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 3, 1, 2, 1, 3, 3, 1, 1, 3, 3, 2, 3, 2, 1, 3, 2, 3, 2, 3, 1, 1]} | 1 |
construct-rg-graph-color-l6-s9 | construct | rg_graph_color | graph_k_coloring | graph_theory | competition | 6 | ReasoningGym/graph_color | Apache-2.0 | [
"agentic_trivial",
"np_search"
] | Colour the vertices of this graph so that no two adjacent vertices have the same colour.
Vertices: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]
Edges: [[0, 14], [0, 19], [1, 4], [1, 15], [1, 30], [2, 8], [2, 17], ... | {"num_vertices": 40, "num_colors": 3, "edges": [[0, 14], [0, 19], [1, 4], [1, 15], [1, 30], [2, 8], [2, 17], [2, 21], [3, 21], [3, 25], [3, 33], [3, 39], [4, 13], [4, 26], [4, 32], [4, 36], [5, 12], [5, 14], [6, 16], [6, 29], [7, 25], [7, 29], [8, 13], [8, 28], [8, 33], [8, 34], [9, 12], [9, 27], [9, 34], [10, 11], [10... | null | null | null | {"coloring": [1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 1, 2, 2, 3, 2, 1, 2, 2, 3, 1, 1, 1, 3, 1, 2, 3, 2, 2, 1, 3, 3, 3, 1, 3, 2, 1, 2]} | 1 |
construct-rg-intermediate-integration-l1-s0 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 1 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = (5*x - 5)**2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ... | {"variable": "x", "integrand": "(5*x - 5)**2", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "25*x**3/3 - 25*x**2 + 25*x + C"} | 1 |
construct-rg-intermediate-integration-l1-s1 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 1 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = (x - 6)**3
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ac... | {"variable": "x", "integrand": "(x - 6)**3", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "x**4/4 - 6*x**3 + 54*x**2 - 216*x + C"} | 1 |
construct-rg-intermediate-integration-l1-s2 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 1 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = (9*x + 8)**3
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ... | {"variable": "x", "integrand": "(9*x + 8)**3", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "729*x**4/4 + 648*x**3 + 864*x**2 + 512*x + C"} | 1 |
construct-rg-intermediate-integration-l1-s3 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 1 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = (4*x - 10)**4
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin,... | {"variable": "x", "integrand": "(4*x - 10)**4", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "256*x**5/5 - 640*x**4 + 3200*x**3 - 8000*x**2 + 10000*x + C"} | 1 |
construct-rg-intermediate-integration-l1-s4 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 1 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 2*(9*x + 5)**3
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin... | {"variable": "x", "integrand": "2*(9*x + 5)**3", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "729*x**4/2 + 810*x**3 + 675*x**2 + 250*x + C"} | 1 |
construct-rg-intermediate-integration-l1-s5 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 1 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -3*(5*x - 4)**2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asi... | {"variable": "x", "integrand": "-3*(5*x - 4)**2", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-25*x**3 + 60*x**2 - 48*x + C"} | 1 |
construct-rg-intermediate-integration-l1-s6 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 1 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -3*(6*x - 9)**2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asi... | {"variable": "x", "integrand": "-3*(6*x - 9)**2", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-36*x**3 + 162*x**2 - 243*x + C"} | 1 |
construct-rg-intermediate-integration-l1-s7 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 1 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -2*(5*x - 4)**4
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asi... | {"variable": "x", "integrand": "-2*(5*x - 4)**4", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-250*x**5 + 1000*x**4 - 1600*x**3 + 1280*x**2 - 512*x + C"} | 1 |
construct-rg-intermediate-integration-l1-s8 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 1 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -3*(8*x - 8)**4
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asi... | {"variable": "x", "integrand": "-3*(8*x - 8)**4", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-12288*x**5/5 + 12288*x**4 - 24576*x**3 + 24576*x**2 - 12288*x + C"} | 1 |
construct-rg-intermediate-integration-l1-s9 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 1 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -3*(5*x + 5)**3
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asi... | {"variable": "x", "integrand": "-3*(5*x + 5)**3", "problem_type": "linear", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-375*x**4/4 - 375*x**3 - 1125*x**2/2 - 375*x + C"} | 1 |
construct-rg-intermediate-integration-l2-s0 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 2 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -6*exp(6*x - 10)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, as... | {"variable": "x", "integrand": "-6*exp(6*x - 10)", "problem_type": "exponential", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-exp(6*x - 10) + C"} | 1 |
construct-rg-intermediate-integration-l2-s1 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 2 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = (18*x - 15)*exp(3*x**2 - 5*x + 4)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions ... | {"variable": "x", "integrand": "(18*x - 15)*exp(3*x**2 - 5*x + 4)", "problem_type": "exponential", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "3*exp(3*x**2 - 5*x + 4) + C"} | 1 |
construct-rg-intermediate-integration-l2-s2 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 2 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 6*sqrt(-6*x - 7)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, as... | {"variable": "x", "integrand": "6*sqrt(-6*x - 7)", "problem_type": "radical", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-2*(-6*x - 7)**(3/2)/3 + C"} | 1 |
construct-rg-intermediate-integration-l2-s3 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 2 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = (36*x - 4)*exp(9*x**2 - 2*x + 6)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions s... | {"variable": "x", "integrand": "(36*x - 4)*exp(9*x**2 - 2*x + 6)", "problem_type": "exponential", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*exp(9*x**2 - 2*x + 6) + C"} | 1 |
construct-rg-intermediate-integration-l2-s4 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 2 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -8*sqrt(5 - 8*x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, as... | {"variable": "x", "integrand": "-8*sqrt(5 - 8*x)", "problem_type": "radical", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*(5 - 8*x)**(3/2)/3 + C"} | 1 |
construct-rg-intermediate-integration-l2-s5 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 2 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -15*sqrt(6 - 5*x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, a... | {"variable": "x", "integrand": "-15*sqrt(6 - 5*x)", "problem_type": "radical", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*(6 - 5*x)**(3/2) + C"} | 1 |
construct-rg-intermediate-integration-l2-s6 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 2 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = (32*x - 10)*exp(8*x**2 - 5*x - 2)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions ... | {"variable": "x", "integrand": "(32*x - 10)*exp(8*x**2 - 5*x - 2)", "problem_type": "exponential", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*exp(8*x**2 - 5*x - 2) + C"} | 1 |
construct-rg-intermediate-integration-l2-s7 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 2 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = (2*x + 5)*exp(x**2 + 5*x - 2)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin,... | {"variable": "x", "integrand": "(2*x + 5)*exp(x**2 + 5*x - 2)", "problem_type": "exponential", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "exp(x**2 + 5*x - 2) + C"} | 1 |
construct-rg-intermediate-integration-l2-s8 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 2 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -8*sqrt(-4*x - 9)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, a... | {"variable": "x", "integrand": "-8*sqrt(-4*x - 9)", "problem_type": "radical", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "4*(-4*x - 9)**(3/2)/3 + C"} | 1 |
construct-rg-intermediate-integration-l2-s9 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 2 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 5*sqrt(5*x - 3)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asi... | {"variable": "x", "integrand": "5*sqrt(5*x - 3)", "problem_type": "radical", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*(5*x - 3)**(3/2)/3 + C"} | 1 |
construct-rg-intermediate-integration-l3-s0 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 3 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 6*sin(3*x - 4)**4*cos(3*x - 4)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin... | {"variable": "x", "integrand": "6*sin(3*x - 4)**4*cos(3*x - 4)", "problem_type": "trigonometric", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*sin(3*x - 4)**5/5 + C"} | 1 |
construct-rg-intermediate-integration-l3-s1 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 3 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -4*sin(2*x + 10)**4*cos(2*x + 10)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions ... | {"variable": "x", "integrand": "-4*sin(2*x + 10)**4*cos(2*x + 10)", "problem_type": "trigonometric", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-2*sin(2*x + 10)**5/5 + C"} | 1 |
construct-rg-intermediate-integration-l3-s2 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 3 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -6*sin(2*x - 2)*cos(2*x - 2)**4
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions si... | {"variable": "x", "integrand": "-6*sin(2*x - 2)*cos(2*x - 2)**4", "problem_type": "trigonometric", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "3*cos(2*x - 2)**5/5 + C"} | 1 |
construct-rg-intermediate-integration-l3-s3 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 3 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 3*sin(x - 3)*cos(x - 3)**2
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, co... | {"variable": "x", "integrand": "3*sin(x - 3)*cos(x - 3)**2", "problem_type": "trigonometric", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-cos(x - 3)**3 + C"} | 1 |
construct-rg-intermediate-integration-l3-s4 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 3 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -7*sin(7*x + 8)**3*cos(7*x + 8)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions si... | {"variable": "x", "integrand": "-7*sin(7*x + 8)**3*cos(7*x + 8)", "problem_type": "trigonometric", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-sin(7*x + 8)**4/4 + C"} | 1 |
construct-rg-intermediate-integration-l3-s5 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 3 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 8*sin(8*x + 3)**2*cos(8*x + 3)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin... | {"variable": "x", "integrand": "8*sin(8*x + 3)**2*cos(8*x + 3)", "problem_type": "trigonometric", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "sin(8*x + 3)**3/3 + C"} | 1 |
construct-rg-intermediate-integration-l3-s6 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 3 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -8*sin(8*x + 2)*cos(8*x + 2)**3
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions si... | {"variable": "x", "integrand": "-8*sin(8*x + 2)*cos(8*x + 2)**3", "problem_type": "trigonometric", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "cos(8*x + 2)**4/4 + C"} | 1 |
construct-rg-intermediate-integration-l3-s7 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 3 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 18*sin(6*x + 3)*cos(6*x + 3)**3
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions si... | {"variable": "x", "integrand": "18*sin(6*x + 3)*cos(6*x + 3)**3", "problem_type": "trigonometric", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-3*cos(6*x + 3)**4/4 + C"} | 1 |
construct-rg-intermediate-integration-l3-s8 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 3 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -7*sin(7*x + 10)**2*cos(7*x + 10)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions ... | {"variable": "x", "integrand": "-7*sin(7*x + 10)**2*cos(7*x + 10)", "problem_type": "trigonometric", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-sin(7*x + 10)**3/3 + C"} | 1 |
construct-rg-intermediate-integration-l3-s9 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 3 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 5*sin(5*x - 10)*cos(5*x - 10)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin,... | {"variable": "x", "integrand": "5*sin(5*x - 10)*cos(5*x - 10)", "problem_type": "trigonometric", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "sin(5*x - 10)**2/2 + C"} | 1 |
construct-rg-intermediate-integration-l4-s0 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 4 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -atan(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos... | {"variable": "x", "integrand": "-atan(x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-x*atan(x) + log(x**2 + 1)/2 + C"} | 1 |
construct-rg-intermediate-integration-l4-s1 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 4 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 2*log(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos... | {"variable": "x", "integrand": "2*log(x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*x*log(x) - 2*x + C"} | 1 |
construct-rg-intermediate-integration-l4-s2 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 4 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -2*atan(2*x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ... | {"variable": "x", "integrand": "-2*atan(2*x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-2*x*atan(2*x) + log(4*x**2 + 1)/2 + C"} | 1 |
construct-rg-intermediate-integration-l4-s3 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 4 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 2*atan(3*x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, a... | {"variable": "x", "integrand": "2*atan(3*x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*x*atan(3*x) - log(9*x**2 + 1)/3 + C"} | 1 |
construct-rg-intermediate-integration-l4-s4 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 4 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -2*atan(2*x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ... | {"variable": "x", "integrand": "-2*atan(2*x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-2*x*atan(2*x) + log(4*x**2 + 1)/2 + C"} | 1 |
construct-rg-intermediate-integration-l4-s5 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 4 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -3*asin(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ac... | {"variable": "x", "integrand": "-3*asin(x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-3*x*asin(x) - 3*sqrt(1 - x**2) + C"} | 1 |
construct-rg-intermediate-integration-l4-s6 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 4 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -asin(3*x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ac... | {"variable": "x", "integrand": "-asin(3*x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-x*asin(3*x) - sqrt(1 - 9*x**2)/3 + C"} | 1 |
construct-rg-intermediate-integration-l4-s7 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 4 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -asin(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos... | {"variable": "x", "integrand": "-asin(x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-x*asin(x) - sqrt(1 - x**2) + C"} | 1 |
construct-rg-intermediate-integration-l4-s8 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 4 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 2*atan(2*x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, a... | {"variable": "x", "integrand": "2*atan(2*x)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*x*atan(2*x) - log(4*x**2 + 1)/2 + C"} | 1 |
construct-rg-intermediate-integration-l4-s9 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 4 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -2*log(x**3)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ... | {"variable": "x", "integrand": "-2*log(x**3)", "problem_type": "log_inverse_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-2*x*log(x**3) + 6*x + C"} | 1 |
construct-rg-intermediate-integration-l5-s0 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 5 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 2*sin(x)*cos(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asi... | {"variable": "x", "integrand": "2*sin(x)*cos(x)", "problem_type": "cyclic", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "sin(x)**2 + C"} | 1 |
construct-rg-intermediate-integration-l5-s1 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 5 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 3*exp(x)*sin(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asi... | {"variable": "x", "integrand": "3*exp(x)*sin(x)", "problem_type": "cyclic", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C"} | 1 |
construct-rg-intermediate-integration-l5-s2 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 5 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 2*x*sin(3*x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ... | {"variable": "x", "integrand": "2*x*sin(3*x)", "problem_type": "polynomial_exp_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-2*x*cos(3*x)/3 + 2*sin(3*x)/9 + C"} | 1 |
construct-rg-intermediate-integration-l5-s3 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 5 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 3*x**2*exp(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin,... | {"variable": "x", "integrand": "3*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "(3*x**2 - 6*x + 6)*exp(x) + C"} | 1 |
construct-rg-intermediate-integration-l5-s4 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 5 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 3*exp(x)*sin(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asi... | {"variable": "x", "integrand": "3*exp(x)*sin(x)", "problem_type": "cyclic", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C"} | 1 |
construct-rg-intermediate-integration-l5-s5 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 5 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 3*x*cos(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, ac... | {"variable": "x", "integrand": "3*x*cos(x)", "problem_type": "polynomial_exp_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "3*x*sin(x) + 3*cos(x) + C"} | 1 |
construct-rg-intermediate-integration-l5-s6 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 5 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -2*exp(x)*sin(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, as... | {"variable": "x", "integrand": "-2*exp(x)*sin(x)", "problem_type": "cyclic", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-exp(x)*sin(x) + exp(x)*cos(x) + C"} | 1 |
construct-rg-intermediate-integration-l5-s7 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 5 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = x*sin(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos... | {"variable": "x", "integrand": "x*sin(x)", "problem_type": "polynomial_exp_trig", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-x*cos(x) + sin(x) + C"} | 1 |
construct-rg-intermediate-integration-l5-s8 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 5 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -3*exp(x)*cos(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, as... | {"variable": "x", "integrand": "-3*exp(x)*cos(x)", "problem_type": "cyclic", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C"} | 1 |
construct-rg-intermediate-integration-l5-s9 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 5 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -sin(x)*cos(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin... | {"variable": "x", "integrand": "-sin(x)*cos(x)", "problem_type": "cyclic", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "-sin(x)**2/2 + C"} | 1 |
construct-rg-intermediate-integration-l6-s0 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 6 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 2*x**5*cos(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin,... | {"variable": "x", "integrand": "2*x**5*cos(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "2*x**5*sin(x) + 10*x**4*cos(x) - 40*x**3*sin(x) - 120*x**2*cos(x) + 240*x*sin(x) + 240*cos(x) + C"} | 1 |
construct-rg-intermediate-integration-l6-s1 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 6 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = -2*x**5*exp(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin... | {"variable": "x", "integrand": "-2*x**5*exp(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "(-2*x**5 + 10*x**4 - 40*x**3 + 120*x**2 - 240*x + 240)*exp(x) + C"} | 1 |
construct-rg-intermediate-integration-l6-s2 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 6 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 2*x**4*exp(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin,... | {"variable": "x", "integrand": "2*x**4*exp(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "(2*x**4 - 8*x**3 + 24*x**2 - 48*x + 48)*exp(x) + C"} | 1 |
construct-rg-intermediate-integration-l6-s3 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 6 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = 3*x**4*cos(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin,... | {"variable": "x", "integrand": "3*x**4*cos(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "3*x**4*sin(x) + 12*x**3*cos(x) - 36*x**2*sin(x) - 72*x*cos(x) + 72*sin(x) + C"} | 1 |
construct-rg-intermediate-integration-l6-s4 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 6 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = x**5*exp(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, a... | {"variable": "x", "integrand": "x**5*exp(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "(x**5 - 5*x**4 + 20*x**3 - 60*x**2 + 120*x - 120)*exp(x) + C"} | 1 |
construct-rg-intermediate-integration-l6-s5 | construct | rg_intermediate_integration | symbolic_antiderivative | analysis | competition | 6 | ReasoningGym/intermediate_integration | Apache-2.0 | [
"symbolic"
] | Find an antiderivative F(x) of
f(x) = x**3*cos(x)
i.e. any F with dF/dx = f(x).
Write the antiderivative as a single expression in the variable x using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, a... | {"variable": "x", "integrand": "x**3*cos(x)", "problem_type": "repeated_parts", "family": "rg_intermediate_integration", "subset": "construct"} | null | null | null | {"antiderivative": "x**3*sin(x) + 3*x**2*cos(x) - 6*x*sin(x) - 6*cos(x) + C"} | 1 |
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