

'''simple docstring'''



from .hash_table import HashTable







class 		lowerCAmelCase__     (   a      ):



 """simple docstring"""



 def __init__(	self      : List[Any]      ,							*__SCREAMING_SNAKE_CASE      : int      ,							**__SCREAMING_SNAKE_CASE      : Union[str, Any]    )						->				Union[str, Any]:


      """simple docstring"""




      super().__init__(*__SCREAMING_SNAKE_CASE      ,							**__SCREAMING_SNAKE_CASE    )


 def    UpperCAmelCase__	(	self      : int      ,							__SCREAMING_SNAKE_CASE      : Dict      ,							__SCREAMING_SNAKE_CASE      : Optional[int]=None    )						->				Dict:


      """simple docstring"""




      __SCREAMING_SNAKE_CASE						     =   1
      __SCREAMING_SNAKE_CASE						     =   self.hash_function(key + i * i    )

      while self.values[new_key] is not None and self.values[new_key] != key:
           i += 1
           __SCREAMING_SNAKE_CASE						     =   (
               self.hash_function(key + i * i    )
               if not self.balanced_factor() >= self.lim_charge
               else None
           )

           if new_key is None:
                break

      return new_key









'''simple docstring'''



from __future__ import annotations

from collections.abc import Callable







def      a__ (						a__   ,					a__   ,					a__   ,					a__ = 1_00   ,					):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE						     =   x_start
     __SCREAMING_SNAKE_CASE						     =   fnc(a__		)
     __SCREAMING_SNAKE_CASE						     =   0.0

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

          # Increment step
          __SCREAMING_SNAKE_CASE						     =   xa
          __SCREAMING_SNAKE_CASE						     =   fxa
     return area


if __name__ == "__main__":







  def      a__ (						a__		):




       """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:')
  UpperCAmelCase				: Optional[Any]         =  1_0
  while i <= 1_0_0_0_0_0:
    UpperCAmelCase				: Union[str, Any]         =  trapezoidal_area(f, -5, 5, i)
    print(f"""with {i} steps: {area}""")
    i *= 1_0






