

'''simple docstring'''

import numpy as np

lowercase__            =     [
    ["a", "b", "c", "d", "e"],
    ["f", "g", "h", "i", "k"],
    ["l", "m", "n", "o", "p"],
    ["q", "r", "s", "t", "u"],
    ["v", "w", "x", "y", "z"],
]




class 			A_					:






     '''simple docstring'''



     def __init__(						self					:	List[Any]			)		->      None:
      UpperCAmelCase			:      int		   =					np.array(lowercase_			)


     def   UpperCAmelCase_			(						self					:	int	,     lowercase_					:	str			)		->      np.ndarray:
      UpperCAmelCase   ,					UpperCAmelCase			:      int		   =					np.where(letter == self.SQUARE			)
      UpperCAmelCase			:      Tuple		   =					np.concatenate([indexa + 1, indexa + 1]			)
      return indexes


     def   UpperCAmelCase_			(						self					:	Optional[Any]	,     lowercase_					:	int	,     lowercase_					:	int			)		->      str:
      return self.SQUARE[indexa - 1, indexa - 1]


     def   UpperCAmelCase_			(						self					:	Optional[int]	,     lowercase_					:	str			)		->      str:
      UpperCAmelCase			:      Optional[Any]		   =					message.lower()
      UpperCAmelCase			:      Any		   =					message.replace('j'	,     'i'			)

      UpperCAmelCase			:      Dict		   =					''
      for letter_index in range(len(lowercase_			)			):
       if message[letter_index] != " ":
        UpperCAmelCase			:      Optional[int]		   =					self.letter_to_numbers(message[letter_index]			)
        UpperCAmelCase			:      Optional[int]		   =					encoded_message + str(numbers[0]			) + str(numbers[1]			)
       elif message[letter_index] == " ":
        UpperCAmelCase			:      Dict		   =					encoded_message + ' '

      return encoded_message




     def   UpperCAmelCase_			(						self					:	List[Any]	,     lowercase_					:	str			)		->      str:
      UpperCAmelCase			:      str		   =					message.replace(' '	,     '  '			)
      UpperCAmelCase			:      List[str]		   =					''
      for numbers_index in range(int(len(lowercase_			) / 2			)			):
       if message[numbers_index * 2] != " ":
        UpperCAmelCase			:      int		   =					message[numbers_index * 2]
        UpperCAmelCase			:      int		   =					message[numbers_index * 2 + 1]

        UpperCAmelCase			:      Optional[Any]		   =					self.numbers_to_letter(int(lowercase_			)	,     int(lowercase_			)			)
        UpperCAmelCase			:      Union[str, Any]		   =					decoded_message + letter
       elif message[numbers_index * 2] == " ":
        UpperCAmelCase			:      List[Any]		   =					decoded_message + ' '

      return decoded_message







'''simple docstring'''

from __future__ import annotations

from collections.abc import Callable




def  UpperCamelCase(	UpperCAmelCase_    ,			UpperCAmelCase_    ,			UpperCAmelCase_    ,			UpperCAmelCase_ = 1_00    ,			):
 UpperCAmelCase			:      Any		   =					x_start
 UpperCAmelCase			:      int		   =					fnc(UpperCAmelCase_      )
 UpperCAmelCase			:      str		   =					0.0

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

  # Increment step
  UpperCAmelCase			:      List[str]		   =					xa
  UpperCAmelCase			:      List[Any]		   =					fxa
 return area


if __name__ == "__main__":




 def  UpperCamelCase(	UpperCAmelCase_      ):
  return x**3

 print("f(x) = x^3")
 print("The area between the curve, x = -10, x = 10 and the x axis is:")
 lowercase__            =     10
 while i <= 100000:
  lowercase__            =     trapezoidal_area(f, -5, 5, i)
  print(f'''with {i} steps: {area}''')
  i *= 10




