



'''simple docstring'''

import math







def 						__UpperCamelCase				(							_lowercase,				_lowercase					) ->			float:
	if (
	    not isinstance(_lowercase,				(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				(							_lowercase,				_lowercase					) ->			float:
	if (
	    not isinstance(_lowercase,				(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 						__UpperCamelCase				(							_lowercase,				_lowercase					) ->			list:
	_lowercase					:       List[str]       =		word.split()

	def justify(_lowercase,				_lowercase,				_lowercase					) -> str:
		_lowercase					:       Dict       =		max_width - width
		_lowercase					:       Tuple       =		len(_lowercase					)
		if len(_lowercase					) == 1:
			# if there is only word in line
			# just insert overall_spaces_count for the remainder of line
			return line[0] + " " * overall_spaces_count
		else:
			_lowercase					:       Tuple       =		words_count - 1
			# num_spaces_between_words_list[i] : tells you to insert
			# num_spaces_between_words_list[i] spaces
			# after word on line[i]
			_lowercase					:       str       =		spaces_to_insert_between_words * [
			    overall_spaces_count // spaces_to_insert_between_words
			]
			_lowercase					:       Optional[int]       =		(
			    overall_spaces_count % spaces_to_insert_between_words
			)
			# distribute spaces via round robin to the left words
			for i in range(_lowercase					):
				num_spaces_between_words_list[i] += 1
			_lowercase					:       Union[str, Any]       =		[]
			for i in range(_lowercase					):
				# add the word
				aligned_words_list.append(line[i]					)
				# add the spaces to insert
				aligned_words_list.append(num_spaces_between_words_list[i] * ' '					)
			# just add the last word to the sentence
			aligned_words_list.append(line[-1]					)
			# join the aligned words list to form a justified line
			return "".join(_lowercase					)

	_lowercase					:       str       =		[]
	_lowercase					:       list[str]       =		[]
	_lowercase					:       Union[str, Any]       =		0
	for word in words:
		if width + len(_lowercase					) + len(_lowercase					) <= max_width:
			# keep adding words until we can fill out max_width
			# width = sum of length of all words (without overall_spaces_count)
			# len(word) = length of current word
			# len(line) = number of overall_spaces_count to insert between words
			line.append(_lowercase					)
			width += len(_lowercase					)
		else:
			# justify the line and add it to result
			answer.append(justify(_lowercase,				_lowercase,				_lowercase					)					)
			# reset new line and new width
			_lowercase  ,    _lowercase					:       Optional[Any]       =		[word], len(_lowercase					)
	_lowercase					:       Optional[int]       =		max_width - width - len(_lowercase					)
	answer.append(' '.join(_lowercase					) + (remaining_spaces + 1) * ' '					)
	return answer


if __name__ == "__main__":
		from doctest import testmod

		testmod()
