




'''simple docstring'''





from __future__ import annotations

import math
from collections.abc import Callable





def       __a      (  _UpperCamelCase:       Callable[[int | float], int | float]   ,		_UpperCamelCase:       int | float   ,		_UpperCamelCase:       int | float   ,		_UpperCamelCase:       int = 100   ,		)		->					float:

     """simple docstring"""




     _snake_case				= x_start
     _snake_case				= fnc(_UpperCamelCase       )
     _snake_case				= 0.0

     for _ in range(_UpperCamelCase       ):
          # Approximates curve as a sequence of linear lines and sums their length
          _snake_case				= (x_end - x_start) / steps + xa
          _snake_case				= fnc(_UpperCamelCase       )
          length += math.hypot(xa - xa   ,		fxa - fxa       )

          # Increment step
          _snake_case				= xa
          _snake_case				= fxa

     return length


if __name__ == "__main__":





   def       __a      (  _UpperCamelCase:       str       )		->					int:

        """simple docstring"""




        return math.sin(10 * x       )

   print('''f(x) = sin(10 * x)''')
   print('''The length of the curve from x = -10 to x = 10 is:''')
   UpperCamelCase_		:     Any          =		10
   while i <= 100000:
      print(F'With {i} steps: {line_length(f, -10, 10, i)}')
      i *= 10








'''simple docstring'''





from math import ceil





def       __a      (  _UpperCamelCase:       int = 1_001       )		->					int:

     """simple docstring"""




     _snake_case				= 1

     for i in range(1   ,		int(ceil(n / 2.0       )       )       ):
          _snake_case				= 2 * i + 1
          _snake_case				= 2 * i
          _snake_case				= total + 4 * odd**2 - 6 * even

     return total


if __name__ == "__main__":
   import sys

   if len(sys.argv) == 1:
      print(solution())
   else:
      try:
         UpperCamelCase_		:     int          =		int(sys.argv[1])
         print(solution(n))
      except ValueError:
         print('''Invalid entry - please enter a number''')


