code: def test_indexed_integrals():
      A = IndexedBase("A")
      i, j = symbols("i j", integer=True)
      a1, a2 = symbols("a1:3", cls=Idx)
      assert isinstance(a1, Idx)
  
      assert IndexedIntegral(1, A[i]).doit() == A[i]
      assert IndexedIntegral(A[i], A[i]).doit() == A[i] ** 2 / 2
      assert IndexedIntegral(A[j], A[i]).doit() == A[i] * A[j]
      assert (
          IndexedIntegral(A[i] * A[j], A[i]).doit()
          == A[i] ** 2 * A[j] / 2
      )
      assert IndexedIntegral(sin(A[i]), A[i]).doit() == -cos(A[i])
      assert IndexedIntegral(sin(A[j]), A[i]).doit() == sin(A[j]) * A[i]
  
      assert IndexedIntegral(1, A[a1]).doit() == A[a1]
      assert IndexedIntegral(A[a1], A[a1]).doit() == A[a1] ** 2 / 2
      assert IndexedIntegral(A[a2], A[a1]).doit() == A[a1] * A[a2]
      assert (
          IndexedIntegral(A[a1] * A[a2], A[a1]).doit()
          == A[a1] ** 2 * A[a2] / 2
      )
      assert IndexedIntegral(sin(A[a1]), A[a1]).doit() == -cos(A[a1])
      assert (
          IndexedIntegral(sin(A[a2]), A[a1]).doit()
          == sin(A[a2]) * A[a1]
      )
  
imports: from sympy.sandbox.indexed_integrals import IndexedIntegral
  from sympy.core.symbol import symbols
  from sympy.functions.elementary.trigonometric import cos, sin
  from sympy.tensor.indexed import Idx, IndexedBase
label_desc: Use image node_id 1 for calling a global function with example usage: test_indexed_integrals() without return types