code: def test_parametric_volumeintegrals():
      cube = ParametricRegion(
          (x, y, z), (x, 0, 1), (y, 0, 1), (z, 0, 1)
      )
      assert ParametricIntegral(1, cube) == 1
  
      solidsphere1 = ParametricRegion(
          (
              r * sin(phi) * cos(theta),
              r * sin(phi) * sin(theta),
              r * cos(phi),
          ),
          (r, 0, 2),
          (theta, 0, 2 * pi),
          (phi, 0, pi),
      )
      solidsphere2 = ParametricRegion(
          (
              r * sin(phi) * cos(theta),
              r * sin(phi) * sin(theta),
              r * cos(phi),
          ),
          (r, 0, 2),
          (phi, 0, pi),
          (theta, 0, 2 * pi),
      )
      assert (
          ParametricIntegral(C.x**2 + C.y**2, solidsphere1)
          == -256 * pi / 15
      )
      assert (
          ParametricIntegral(C.x**2 + C.y**2, solidsphere2)
          == 256 * pi / 15
      )
  
      region_under_plane1 = ParametricRegion(
          (x, y, z),
          (x, 0, 3),
          (y, 0, -2 * x / 3 + 2),
          (z, 0, 6 - 2 * x - 3 * y),
      )
      region_under_plane2 = ParametricRegion(
          (x, y, z),
          (x, 0, 3),
          (z, 0, 6 - 2 * x - 3 * y),
          (y, 0, -2 * x / 3 + 2),
      )
  
      assert ParametricIntegral(
          C.x * C.i + C.j - 100 * C.k, region_under_plane1
      ) == ParametricIntegral(
          C.x * C.i + C.j - 100 * C.k, region_under_plane2
      )
      assert ParametricIntegral(2 * C.x, region_under_plane2) == -9
  
file_path: sympy/sympy/vector/tests/test_integrals.py
imports: from sympy.core.numbers import pi
  from sympy.core.singleton import S
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import cos, sin
  from sympy.testing.pytest import raises
  from sympy.vector.coordsysrect import CoordSys3D
  from sympy.vector.integrals import ParametricIntegral, vector_integrate
  from sympy.vector.parametricregion import ParametricRegion
  from sympy.vector.implicitregion import ImplicitRegion
  from sympy.abc import x, y, z, u, v, r, t, theta, phi
  from sympy.geometry import Point, Segment, Curve, Circle, Polygon, Plane
label_desc: Use image node_id 3 for calling a global function with example usage: test_parametric_volumeintegrals() without return types