






'''simple docstring'''
import math




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   if (
       not isinstance(_UpperCamelCase						,		(int, float)							)
       or power_factor < -1
       or power_factor > 1
   ):
      raise ValueError("power_factor must be a valid float value between -1 and 1."							)
   return apparent_power * power_factor




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   if (
       not isinstance(_UpperCamelCase						,		(int, float)							)
       or power_factor < -1
       or power_factor > 1
   ):
      raise ValueError("power_factor must be a valid float value between -1 and 1."							)
   return apparent_power * math.sqrt(1 - power_factor**2							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()












'''simple docstring'''
def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase = 200							):


   """simple docstring"""




   lowercase_	:    Optional[int]           =     [1, 2, 5, 10, 20, 50, 100, 200]
   lowercase_	:    str           =     [0] * (pence + 1)
   lowercase_	:    Dict           =     1  # base case: 1 way to make 0 pence

   for coin in coins:
      for i in range(_UpperCamelCase						,		pence + 1						,		1							):
         number_of_ways[i] += number_of_ways[i - coin]
   return number_of_ways[pence]


if __name__ == "__main__":
 assert solution(200) == 73682




