code: def _basic_simpson(y, start, stop, x, dx, axis):
      nd = len(y.shape)
      if start is None:
          start = 0
      step = 2
      slice_all = (slice(None),) * nd
      slice0 = tupleset(slice_all, axis, slice(start, stop, step))
      slice1 = tupleset(
          slice_all, axis, slice(start + 1, stop + 1, step)
      )
      slice2 = tupleset(
          slice_all, axis, slice(start + 2, stop + 2, step)
      )
  
      if x is None:  # Even-spaced Simpson's rule.
          result = np.sum(
              y[slice0] + 4 * y[slice1] + y[slice2], axis=axis
          )
          result *= dx / 3.0
      else:
          # Account for possibly different spacings.
          #    Simpson's rule changes a bit.
          h = np.diff(x, axis=axis)
          sl0 = tupleset(slice_all, axis, slice(start, stop, step))
          sl1 = tupleset(
              slice_all, axis, slice(start + 1, stop + 1, step)
          )
          h0 = h[sl0]
          h1 = h[sl1]
          hsum = h0 + h1
          hprod = h0 * h1
          h0divh1 = h0 / h1
          tmp = (
              hsum
              / 6.0
              * (
                  y[slice0] * (2 - 1.0 / h0divh1)
                  + y[slice1] * (hsum * hsum / hprod)
                  + y[slice2] * (2 - h0divh1)
              )
          )
          result = np.sum(tmp, axis=axis)
      return result
  
imports: from __future__ import annotations
  from typing import TYPE_CHECKING, Callable, Dict, Tuple, Any, cast
  import functools
  import numpy
  import math
  import types
  import warnings
  from numpy import trapz
  from scipy.special import roots_legendre
  from scipy.special import gammaln
label_desc: Use image node_id 11 for calling a global function with example usage: _basic_simpson(y, start, stop, x, dx, axis) and returns: result