
'''simple docstring'''





def 					UpperCamelCase_(     snake_case							:	float					):

							'''simple docstring'''






							if edge <= 0 or not isinstance(snake_case							,    snake_case					):
														raise ValueError("Length must be a positive."					)
							return 3 * ((2_5 + 1_0 * (5 ** (1 / 2))) ** (1 / 2)) * (edge**2)


def 					UpperCamelCase_(     snake_case							:	float					):

							'''simple docstring'''






							if edge <= 0 or not isinstance(snake_case							,    snake_case					):
														raise ValueError("Length must be a positive."					)
							return ((1_5 + (7 * (5 ** (1 / 2)))) / 4) * (edge**3)


if __name__ == "__main__":
		import doctest

		doctest.testmod()










'''simple docstring'''





def 					UpperCamelCase_(     snake_case							:	list[int]							,    snake_case							:	int					):

							'''simple docstring'''






							snake_case_      =				len(snake_case					)
							snake_case_      =				[[False] * (required_sum + 1) for _ in range(arr_len + 1					)]

							# for each arr value, a sum of zero(0) can be formed by not taking any element
							# hence True/1
							for i in range(arr_len + 1					):
														snake_case_      =				True

							# sum is not zero and set is empty then false
							for i in range(1							,    required_sum + 1					):
														snake_case_      =				False

							for i in range(1							,    arr_len + 1					):
														for j in range(1							,    required_sum + 1					):
																					if arr[i - 1] > j:
																												snake_case_      =				subset[i - 1][j]
																					if arr[i - 1] <= j:
																												snake_case_      =				subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

							return subset[arr_len][required_sum]


if __name__ == "__main__":
		import doctest

		doctest.testmod()




