






"""simple docstring"""





UpperCamelCase					=     10_00






def 							A(    snake_case_						):
       """simple docstring"""





       return x * x






def 							A(    snake_case_		,  snake_case_		,  snake_case_		,  snake_case_ = 4						):
       """simple docstring"""





       assert callable(
           snake_case_						), F"""the function(object) passed should be callable your input : {function}"""
       assert isinstance(snake_case_		,  (float, int)						), F"""a should be float or integer your input : {a}"""
       assert isinstance(function(snake_case_						)		,  (float, int)						), (
           "the function should return integer or float return type of your function, "
           F"""{type(snake_case_						)}"""
       )
       assert isinstance(snake_case_		,  (float, int)						), F"""b should be float or integer your input : {b}"""
       assert (
           isinstance(snake_case_		,  snake_case_						) and precision > 0
       ), F"""precision should be positive integer your input : {precision}"""

       # just applying the formula of simpson for approximate integration written in
       # mentioned article in first comment of this file and above this function

       lowercase__:							Optional[int]         =     (b - a) / N_STEPS
       lowercase__:							str         =     function(snake_case_						) + function(snake_case_						)

       for i in range(1		,  snake_case_						):
              lowercase__:							Optional[Any]         =     a + h * i
              result += function(snake_case_						) * (4 if i % 2 else 2)

       result *= h / 3
       return round(snake_case_		,  snake_case_						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()










import numpy as np

_UpperCAmelCase      :	int  =[
    ["""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 					snake_case__:







						'''simple docstring'''




						def __init__(					self				)       ->     None:
										lowerCAmelCase_			:   List[Any]     					=					np.array(__lowercase				)




						def     lowercase_			(					self ,    __lowercase				)       ->     np.ndarray:
										lowerCAmelCase_					,	lowerCAmelCase_			:   List[str]     					=					np.where(letter == self.SQUARE				)
										lowerCAmelCase_			:   Union[str, Any]     					=					np.concatenate([indexa + 1, indexa + 1]				)
										return indexes




						def     lowercase_			(					self ,    __lowercase ,    __lowercase				)       ->     str:
										return self.SQUARE[indexa - 1, indexa - 1]




						def     lowercase_			(					self ,    __lowercase				)       ->     str:
										lowerCAmelCase_			:   Dict     					=					message.lower()
										lowerCAmelCase_			:   Any     					=					message.replace('''j''' ,    '''i'''				)

										lowerCAmelCase_			:   Optional[Any]     					=					''''''
										for letter_index in range(len(__lowercase				)				):
														if message[letter_index] != " ":
																		lowerCAmelCase_			:   Optional[Any]     					=					self.letter_to_numbers(message[letter_index]				)
																		lowerCAmelCase_			:   List[Any]     					=					encoded_message + str(numbers[0]				) + str(numbers[1]				)
														elif message[letter_index] == " ":
																		lowerCAmelCase_			:   Optional[Any]     					=					encoded_message + ''' '''

										return encoded_message




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

																		lowerCAmelCase_			:   Dict     					=					self.numbers_to_letter(int(__lowercase				) ,    int(__lowercase				)				)
																		lowerCAmelCase_			:   Tuple     					=					decoded_message + letter
														elif message[numbers_index * 2] == " ":
																		lowerCAmelCase_			:   List[str]     					=					decoded_message + ''' '''

										return decoded_message