





'''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			,	)							->     float:

       """simple docstring"""


       UpperCAmelCase  =						x_start
       UpperCAmelCase  =						fnc(SCREAMING_SNAKE_CASE_ )
       UpperCAmelCase  =						0.0
       for _ in range(SCREAMING_SNAKE_CASE_ ):
              # Approximates small segments of curve as linear and solve
              # for trapezoidal area
              UpperCAmelCase  =						(x_end - x_start) / steps + xa
              UpperCAmelCase  =						fnc(SCREAMING_SNAKE_CASE_ )
              area += abs(fxa + fxa ) * (xa - xa) / 2
              # Increment step
              UpperCAmelCase  =						xa
              UpperCAmelCase  =						fxa
       return area


if __name__ == "__main__":
    def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Optional[Any] )							->     List[str]:

           """simple docstring"""


           return x**3 + x**2

    print('f(x) = x^3 + x^2')
    print('The area between the curve, x = -5, x = 5 and the x axis is:')
    a__			:					Union[str, Any]       						=						10
    while i <= 100_000:
        print(F"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
        i *= 10






'''simple docstring'''
def 					lowerCamelCase_ ( __UpperCamelCase					:       int		)					->	list:







     """simple docstring"""
     _A				=							int(__UpperCamelCase		)
     if n_element < 1:
          _A				=							ValueError('a should be a positive number'		)
          raise my_error

     _A				=							[1]
     _A		,				_A		,				_A				=							(0, 0, 0)
     _A				=							1
     while index < n_element:
          while hamming_list[i] * 2 <= hamming_list[-1]:
               i += 1
          while hamming_list[j] * 3 <= hamming_list[-1]:
               j += 1
          while hamming_list[k] * 5 <= hamming_list[-1]:
               k += 1
          hamming_list.append(
              min(hamming_list[i] * 2							,    hamming_list[j] * 3							,    hamming_list[k] * 5		)		)
          index += 1
     return hamming_list


if __name__ == "__main__":
    lowerCAmelCase						=					input("""Enter the last number (nth term) of the Hamming Number Series: """)
    print("""Formula of Hamming Number Series => 2^i * 3^j * 5^k""")
    lowerCAmelCase						=					hamming(int(n))
    print("""-----------------------------------------------------""")
    print(F'The list with nth numbers is: {hamming_numbers}')
    print("""-----------------------------------------------------""")





