






"""simple docstring"""



def 		_SCREAMING_SNAKE_CASE					(       __snake_case     :    List[Any]						,   __snake_case     :    str       ):





  '''simple docstring'''





  if n < 0:
    return 0
  # table[i] represents the number of ways to get to amount i
  lowercase				       =			[0] * (n + 1)

  # There is exactly 1 way to get to zero(You pick no coins).
  lowercase				       =			1

  # Pick all coins one by one and update table[] values
  # after the index greater than or equal to the value of the
  # picked coin
  for coin_val in s:
    for j in range(__snake_case						,   n + 1       ):
      table[j] += table[j - coin_val]

  return table[n]


if __name__ == "__main__":
    import doctest

    doctest.testmod()









'''simple docstring'''


from __future__ import annotations

from collections.abc import Callable




def       A							(      _UpperCAmelCase   :				Callable[[int | float], int | float]						,_UpperCAmelCase   :				int | float						,_UpperCAmelCase   :				int | float						,_UpperCAmelCase   :				int = 1_0_0						,)  ->				float:


  '''simple docstring'''




  __lowerCAmelCase		:    Dict			     =  x_start
  __lowerCAmelCase		:    Tuple			     =  fnc(_UpperCAmelCase					)
  __lowerCAmelCase		:    Optional[int]			     =  0.0

  for _ in range(_UpperCAmelCase					):
    # Approximates small segments of curve as linear and solve
    # for trapezoidal area
    __lowerCAmelCase		:    Optional[int]			     =  (x_end - x_start) / steps + xa
    __lowerCAmelCase		:    Optional[Any]			     =  fnc(_UpperCAmelCase					)
    area += abs(fxa + fxa					) * (xa - xa) / 2

    # Increment step
    __lowerCAmelCase		:    Optional[Any]			     =  xa
    __lowerCAmelCase		:    List[Any]			     =  fxa
  return area


if __name__ == "__main__":




    def       A							(      _UpperCAmelCase   :				List[Any]					)  ->				List[Any]:


      '''simple docstring'''




      return x**3

    print("f(x) = x^3")
    print("The area between the curve, x = -10, x = 10 and the x axis is:")
    A_				     =							10
    while i <= 10_00_00:
        A_				     =							trapezoidal_area(f, -5, 5, i)
        print(F'''with {i} steps: {area}''')
        i *= 10





