




'''simple docstring'''

from __future__ import annotations




def    _a    (							lowerCAmelCase_ = 4	):





      """simple docstring"""



      _snake_case		:	List[Any]					     =     abs(lowerCAmelCase_	) or 4
      return [[1 + x + y * row_size for x in range(lowerCAmelCase_	)] for y in range(lowerCAmelCase_	)]




def    _a    (							lowerCAmelCase_	):





      """simple docstring"""



      return reverse_row(transpose(lowerCAmelCase_	)	)
      # OR.. transpose(reverse_column(matrix))




def    _a    (							lowerCAmelCase_	):





      """simple docstring"""



      return reverse_row(reverse_column(lowerCAmelCase_	)	)
      # OR.. reverse_column(reverse_row(matrix))




def    _a    (							lowerCAmelCase_	):





      """simple docstring"""



      return reverse_column(transpose(lowerCAmelCase_	)	)
      # OR.. transpose(reverse_row(matrix))




def    _a    (							lowerCAmelCase_	):





      """simple docstring"""



      _snake_case		:	Tuple					     =     [list(lowerCAmelCase_	) for x in zip(*lowerCAmelCase_	)]
      return matrix




def    _a    (							lowerCAmelCase_	):





      """simple docstring"""



      _snake_case		:	Dict					     =     matrix[::-1]
      return matrix




def    _a    (							lowerCAmelCase_	):





      """simple docstring"""



      _snake_case		:	Optional[int]					     =     [x[::-1] for x in matrix]
      return matrix




def    _a    (							lowerCAmelCase_	):





      """simple docstring"""



      for i in matrix:
            print(*lowerCAmelCase_	)


if __name__ == "__main__":
   UpperCAmelCase					:		Dict		=							make_matrix()
   print('\norigin:\n')
   print_matrix(matrix)
   print('\nrotate 90 counterclockwise:\n')
   print_matrix(rotate_aa(matrix))

   UpperCAmelCase					:		List[str]		=							make_matrix()
   print('\norigin:\n')
   print_matrix(matrix)
   print('\nrotate 180:\n')
   print_matrix(rotate_aaa(matrix))

   UpperCAmelCase					:		List[str]		=							make_matrix()
   print('\norigin:\n')
   print_matrix(matrix)
   print('\nrotate 270 counterclockwise:\n')
   print_matrix(rotate_aaa(matrix))









'''simple docstring'''

import math

from numpy import inf
from scipy.integrate import quad




def    _a    (							lowerCAmelCase_	):





      """simple docstring"""



      if num <= 0:
            raise ValueError('''math domain error'''	)

      return quad(lowerCAmelCase_			,      0			,      lowerCAmelCase_			,      args=(lowerCAmelCase_)	)[0]




def    _a    (							lowerCAmelCase_			,      lowerCAmelCase_	):





      """simple docstring"""



      return math.pow(lowerCAmelCase_			,      z - 1	) * math.exp(-x	)


if __name__ == "__main__":
   from doctest import testmod

   testmod()


