

'''simple docstring'''




def 							lowerCamelCase			(   UpperCAmelCase__ :      float				)    ->   float:

							if edge <= 0 or not isinstance(UpperCAmelCase__   ,   UpperCAmelCase__				):
														raise ValueError("""Length must be a positive."""				)
							return 3 * ((25 + 10 * (5 ** (1 / 2))) ** (1 / 2)) * (edge**2)




def 							lowerCamelCase			(   UpperCAmelCase__ :      float				)    ->   float:

							if edge <= 0 or not isinstance(UpperCAmelCase__   ,   UpperCAmelCase__				):
														raise ValueError("""Length must be a positive."""				)
							return ((15 + (7 * (5 ** (1 / 2)))) / 4) * (edge**3)


if __name__ == "__main__":
						import doctest

						doctest.testmod()






'''simple docstring'''




from collections.abc import Callable

import numpy as np




def 							lowerCamelCase			(   UpperCAmelCase__ :      Callable   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float   ,   UpperCAmelCase__ :      float				)    ->   np.array:
							lowercase_      :    Any       		= int(np.ceil((x_end - xa) / step_size				)				)
							lowercase_      :    List[Any]       		= np.zeros((n + 1,)				)
							lowercase_      :    List[Any]       		= ya
							lowercase_      :    List[str]       		= xa

							for k in range(UpperCAmelCase__				):
														lowercase_      :    Optional[Any]       		= y[k] + step_size * ode_func(UpperCAmelCase__   ,   y[k]				)
														lowercase_      :    List[Any]       		= y[k] + (
														    (step_size / 2) * (ode_func(UpperCAmelCase__   ,   y[k]				) + ode_func(x + step_size   ,   UpperCAmelCase__				))
														)
														x += step_size

							return y


if __name__ == "__main__":
						import doctest

						doctest.testmod()





