






from __future__ import annotations






def 							lowerCamelCase__ (       __lowerCamelCase     :	int    ,						__lowerCamelCase     :	int						):
  if partitions <= 0:
    raise ValueError("""partitions must be a positive number!"""						)
  if partitions > number_of_bytes:
    raise ValueError("""partitions can not > number_of_bytes!"""						)
  __UpperCAmelCase				:      int	 =    number_of_bytes // partitions
  __UpperCAmelCase				:      str	 =    []
  for i in range(__lowerCamelCase						):
    __UpperCAmelCase				:      Optional[Any]	 =    i * bytes_per_partition + 1
    __UpperCAmelCase				:      Any	 =    (
        number_of_bytes if i == partitions - 1 else (i + 1) * bytes_per_partition
    )
    allocation_list.append(f"""{start_bytes}-{end_bytes}"""						)
  return allocation_list


if __name__ == "__main__":
       import doctest

       doctest.testmod()




"""simple docstring"""





from collections.abc import Callable

import numpy as np



def  lowerCamelCase__						(     __snake_case,	__snake_case,	__snake_case,	__snake_case,	__snake_case      )				->						np.array:


					"""simple docstring"""





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

					for k in range(__snake_case      ):
										_UpperCamelCase									=    y[k] + step_size * ode_func(__snake_case,	y[k]      )
										_UpperCamelCase									=    y[k] + (
										    (step_size / 2) * (ode_func(__snake_case,	y[k]      ) + ode_func(x + step_size,	__snake_case      ))
										)
										x += step_size

					return y


if __name__ == "__main__":
				import doctest

				doctest.testmod()






