

from collections.abc import Callable

import numpy as np





def 					__lowerCamelCase	( UpperCamelCase__   ,							UpperCamelCase__   ,							UpperCamelCase__   ,							UpperCamelCase__   ,							UpperCamelCase__      ):







							'''simple docstring'''






							snake_case_							=    int(np.ceil((x_end - xa) / step_size      )      )
							snake_case_							=    np.zeros((n + 1,)      )
							snake_case_							=    ya
							snake_case_							=    xa

							for k in range(UpperCamelCase__      ):
														snake_case_							=    y[k] + step_size * ode_func(UpperCamelCase__   ,							y[k]      )
														snake_case_							=    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()







def 					__lowerCamelCase	( UpperCamelCase__      ):







							'''simple docstring'''






							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__      ):







							'''simple docstring'''






							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()




