




from .imports import is_rich_available


if is_rich_available():
      from rich.traceback import install

      install(show_locals=False)

else:
      raise ModuleNotFoundError("""To use the rich extension, install rich with `pip install rich`""")







import numpy as np
def 		a_							( __lowerCAmelCase   , __lowerCAmelCase   , __lowerCAmelCase   , __lowerCAmelCase   , __lowerCAmelCase				):
  lowerCAmelCase__										=      int(np.ceil((x_end - xa) / h				)				)
  lowerCAmelCase__										=      np.zeros((n + 1,)				)
  lowerCAmelCase__										=      ya
  lowerCAmelCase__										=      xa

  for k in range(__lowerCAmelCase				):
    lowerCAmelCase__										=      f(__lowerCAmelCase   , y[k]				)
    lowerCAmelCase__										=      f(x + 0.5 * h   , y[k] + 0.5 * h * ka				)
    lowerCAmelCase__										=      f(x + 0.5 * h   , y[k] + 0.5 * h * ka				)
    lowerCAmelCase__										=      f(x + h   , y[k] + h * ka				)
    lowerCAmelCase__										=      y[k] + (1 / 6) * h * (ka + 2 * ka + 2 * ka + ka)
    x += h

  return y


if __name__ == "__main__":
      import doctest

      doctest.testmod()

