


import math

def 						_UpperCAmelCase				(			SCREAMING_SNAKE_CASE__			:					float			,     SCREAMING_SNAKE_CASE__			:					float				):
     if (
         not isinstance(SCREAMING_SNAKE_CASE__			,     (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 						_UpperCAmelCase				(			SCREAMING_SNAKE_CASE__			:					float			,     SCREAMING_SNAKE_CASE__			:					float				):
     if (
         not isinstance(SCREAMING_SNAKE_CASE__			,     (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()









def 						_UpperCAmelCase				(			SCREAMING_SNAKE_CASE__			:					int = 10**12				):
     __UpperCamelCase    							=1
     __UpperCamelCase    							=0

     __UpperCamelCase    							=1
     __UpperCamelCase    							=1

     while numerator <= 2 * min_total - 1:
          prev_numerator += 2 * numerator
          numerator += 2 * prev_numerator

          prev_denominator += 2 * denominator
          denominator += 2 * prev_denominator

     return (denominator + 1) // 2


if __name__ == "__main__":
   print(f"""{solution() = }""")





