code: 
  
  
  
  """simple docstring"""
  
  
  
  
  from __future__ import annotations
  
  from collections.abc import Callable
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		Callable[[int | float], int | float]		,						SCREAMING_SNAKE_CASE__			:		int | float		,						SCREAMING_SNAKE_CASE__			:		int | float		,						SCREAMING_SNAKE_CASE__			:		int = 100		,						)						->     Dict:
  
  
  
  
  
       '''simple docstring'''
  
       _UpperCAmelCase    :			List[Any]              =					x_start
       _UpperCAmelCase    :			str              =					fnc(lowercase__       )
       _UpperCAmelCase    :			Dict              =					0.0
  
       for _ in range(lowercase__       ):
            # Approximates small segments of curve as linear and solve
            # for trapezoidal area
            _UpperCAmelCase    :			Any              =					(x_end - x_start) / steps + xa
            _UpperCAmelCase    :			Union[str, Any]              =					fnc(lowercase__       )
            area += abs(fxa + fxa       ) * (xa - xa) / 2
  
            # Increment step
            _UpperCAmelCase    :			Optional[int]              =					xa
            _UpperCAmelCase    :			Optional[int]              =					fxa
       return area
  
  
  if __name__ == "__main__":
  
   def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		Optional[Any]       )						->     str:
  
  
  
  
  
        '''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:")
   _lowerCAmelCase       :      Tuple							=							10
   while i <= 10_00_00:
    _lowerCAmelCase       :      Dict							=							trapezoidal_area(f, -5, 5, i)
    print(F"with {i} steps: {area}")
    i *= 10
  
style_context: 
  
  
  
  """simple docstring"""
  
  
  
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		list       )						->     bool:
  
  
  
  
  
       '''simple docstring'''
  
       if not isinstance(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       ):
            raise ValueError("Input series is not valid, valid series - [1, 2/3, 2]"       )
       if len(SCREAMING_SNAKE_CASE__       ) == 0:
            raise ValueError("Input list must be a non empty list"       )
       if len(SCREAMING_SNAKE_CASE__       ) == 1 and series[0] != 0:
            return True
       _UpperCAmelCase    :			Tuple              =					[]
       _UpperCAmelCase    :			Any              =					len(SCREAMING_SNAKE_CASE__       )
       for i in range(0		,						SCREAMING_SNAKE_CASE__       ):
            if series[i] == 0:
                 raise ValueError("Input series cannot have 0 as an element"       )
            rec_series.append(1 / series[i]       )
       _UpperCAmelCase    :			Dict              =					rec_series[1] - rec_series[0]
       for index in range(2		,						SCREAMING_SNAKE_CASE__       ):
            if rec_series[index] - rec_series[index - 1] != common_diff:
                 return False
       return True
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		list       )						->     float:
  
  
  
  
  
       '''simple docstring'''
  
       if not isinstance(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       ):
            raise ValueError("Input series is not valid, valid series - [2, 4, 6]"       )
       if len(SCREAMING_SNAKE_CASE__       ) == 0:
            raise ValueError("Input list must be a non empty list"       )
       _UpperCAmelCase    :			Any              =					0
       for val in series:
            answer += 1 / val
       return len(SCREAMING_SNAKE_CASE__       ) / answer
  
  
  if __name__ == "__main__":
   import doctest
  
   doctest.testmod()
  