"""simple docstring"""





from collections.abc import Callable

import numpy as np





def 				a_     (      _lowerCAmelCase  : Callable   , _lowerCAmelCase  : float   , _lowerCAmelCase  : float   , _lowerCAmelCase  : float   , _lowerCAmelCase  : float     ):





       '''simple docstring'''

       lowercase__			:		List[str]       =	int(np.ceil((x_end - xa) / step_size     )     )
       lowercase__			:		List[Any]       =	np.zeros((n + 1,)     )
       lowercase__			:		Union[str, Any]       =	ya
       lowercase__			:		List[Any]       =	xa

       for k in range(_lowerCAmelCase     ):
              lowercase__			:		Any       =	y[k] + step_size * ode_func(_lowerCAmelCase   , y[k]     )
              x += step_size

       return y


if __name__ == "__main__":
       import doctest

       doctest.testmod()




from __future__ import annotations

from math import pi, sqrt


def   __SCREAMING_SNAKE_CASE					(SCREAMING_SNAKE_CASE__  ,		SCREAMING_SNAKE_CASE__       ):

						if inductance <= 0:
												raise ValueError('''Inductance cannot be 0 or negative'''       )

						elif capacitance <= 0:
												raise ValueError('''Capacitance cannot be 0 or negative'''       )

						else:
												return (
												    "Resonant frequency",
												    float(1 / (2 * pi * (sqrt(inductance * capacitance       )))       ),
												)


if __name__ == "__main__":
					import doctest

					doctest.testmod()