
'''simple docstring'''
from __future__ import annotations

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						):
    """simple docstring"""






    if not all((nth_term, start_term_a, common_ratio_r)    ):
        return []
    snake_case_	:      list[float | int]            =  []
    snake_case_	:      Optional[int]            =  1
    snake_case_	:      Union[str, Any]            =  common_ratio_r
    for _ in range(int(__SCREAMING_SNAKE_CASE    )    ):
        if not series:
            series.append(__SCREAMING_SNAKE_CASE    )
        else:
            power += 1
            series.append(float(start_term_a * multiple    )    )
            snake_case_	:      Optional[Any]            =  pow(float(__SCREAMING_SNAKE_CASE    ),						__SCREAMING_SNAKE_CASE    )
    return series


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  a_     =  float(input("Enter the last number (n term) of the Geometric Series"))
  a_     =  float(input("Enter the starting term (a) of the Geometric Series"))
  a_     =  float(
      input("Enter the common ratio between two terms (r) of the Geometric Series")
  )
  print("Formula of Geometric Series => a + ar + ar^2 ... +ar^n")
  print(geometric_series(nth_term, start_term_a, common_ratio_r))






'''simple docstring'''
from __future__ import annotations

from collections.abc import Callable

def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE,						__SCREAMING_SNAKE_CASE = 1_0_0,						):
    """simple docstring"""






    snake_case_	:      Optional[Any]            =  x_start
    snake_case_	:      str            =  fnc(__SCREAMING_SNAKE_CASE    )
    snake_case_	:      List[str]            =  0.0

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

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


if __name__ == "__main__":

  def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
      """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_0000:
    a_     =  trapezoidal_area(f, -5, 5, i)
    print(f"""with {i} steps: {area}""")
    i *= 10




