code: def test_main_integrate():
      triangle = Polygon((0, 3), (5, 3), (1, 1))
      facets = triangle.sides
      hp_params = hyperplane_parameters(triangle)
      assert main_integrate(
          x**2 + y**2, facets, hp_params
      ) == Rational(325, 6)
      assert main_integrate(
          x**2 + y**2, facets, hp_params, max_degree=1
      ) == {0: 0, 1: 5, y: Rational(35, 3), x: 10}
  
imports: from sympy.functions.elementary.complexes import Abs
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.core import S, Rational
  from sympy.integrals.intpoly import decompose, best_origin, distance_to_side, polytope_integrate, point_sort, hyperplane_parameters, main_integrate3d, main_integrate, polygon_integrate, lineseg_integrate, integration_reduction, integration_reduction_dynamic, is_vertex
  from sympy.geometry.line import Segment2D
  from sympy.geometry.polygon import Polygon
  from sympy.geometry.point import Point, Point2D
  from sympy.abc import x, y, z
  from sympy.testing.pytest import slow
label_desc: Use image node_id 8 for calling a global function with example usage: test_main_integrate() without return types