
'''simple docstring'''
from __future__ import annotations

from collections.abc import Callable




def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__      ,    SCREAMING_SNAKE_CASE__ = 100      ,    )   ->				float:


		'''simple docstring'''


		snake_case   :    int			       =		x_start
		snake_case   :    Tuple			       =		fnc(SCREAMING_SNAKE_CASE__       )
		snake_case   :    Dict			       =		0.0

		for _ in range(SCREAMING_SNAKE_CASE__       ):
				# Approximates small segments of curve as linear and solve
				# for trapezoidal area
				snake_case   :    str			       =		(x_end - x_start) / steps + xa
				snake_case   :    str			       =		fnc(SCREAMING_SNAKE_CASE__       )
				area += abs(fxa + fxa       ) * (xa - xa) / 2

				# Increment step
				snake_case   :    Any			       =		xa
				snake_case   :    List[str]			       =		fxa
		return area


if __name__ == "__main__":




						def 					_UpperCamelCase		(    SCREAMING_SNAKE_CASE__       )   ->				str:


								'''simple docstring'''


								return x**3

						print("f(x) = x^3")
						print("The area between the curve, x = -10, x = 10 and the x axis is:")
						lowercase__		    =	1_0
						while i <= 1_0_0_0_0_0:
												lowercase__		    =	trapezoidal_area(f, -5, 5, i)
												print(f"with {i} steps: {area}")
												i *= 1_0








'''simple docstring'''



def 	_UpperCamelCase       (_lowerCamelCase							:   list[list[int]]      ,		_lowerCamelCase							:   list[list[int]]		)->      list[list[int]]:




     '''simple docstring'''





     __snake_case			    =     []
     __snake_case			    =     len(_lowerCamelCase		)
     for i in range(_lowerCamelCase		):
          __snake_case			    =     []
          for j in range(_lowerCamelCase		):
               __snake_case			    =     0
               for k in range(_lowerCamelCase		):
                    __snake_case			    =     val + matrix_a[i][k] * matrix_b[k][j]
               list_a.append(_lowerCamelCase		)
          matrix_c.append(_lowerCamelCase		)
     return matrix_c







def 	_UpperCamelCase       (_lowerCamelCase							:   int		)->      list[list[int]]:




     '''simple docstring'''





     return [[int(row == column		) for column in range(_lowerCamelCase		)] for row in range(_lowerCamelCase		)]







def 	_UpperCamelCase       (_lowerCamelCase							:   int		)->      int:




     '''simple docstring'''





     if n <= 1:
          return n
     __snake_case			    =     identity(2		)
     __snake_case			    =     [[1, 1], [1, 0]]
     __snake_case			    =     n - 1
     while n > 0:
          if n % 2 == 1:
               __snake_case			    =     multiply(_lowerCamelCase      ,		_lowerCamelCase		)
          __snake_case			    =     multiply(_lowerCamelCase      ,		_lowerCamelCase		)
          __snake_case			    =     int(n / 2		)
     return res_matrix[0][0]







def 	_UpperCamelCase       (_lowerCamelCase							:   int		)->      int:




     '''simple docstring'''





     if n <= 1:
          return n
     __snake_case			    =     0
     __snake_case			    =     1
     for _ in range(2      ,		n + 1		):
          __snake_case    ,			__snake_case			    =     fiba, fiba + fiba
     return fiba







def 	_UpperCamelCase       ()->      None:




     '''simple docstring'''





     for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
          __snake_case			    =     int(''''''.join(c for c in ordinal if c in '''0123456789'''		)		)  # 1000th --> 1000
          print(
              f'''{ordinal} fibonacci number using matrix exponentiation is '''
              f'''{nth_fibonacci_matrix(_lowerCamelCase		)} and using bruteforce is '''
              f'''{nth_fibonacci_bruteforce(_lowerCamelCase		)}\n'''		)
     # from timeit import timeit
     # print(timeit("nth_fibonacci_matrix(1000000)",
     #              "from main import nth_fibonacci_matrix", number=5))
     # print(timeit("nth_fibonacci_bruteforce(1000000)",
     #              "from main import nth_fibonacci_bruteforce", number=5))
     # 2.3342058970001744
     # 57.256506615000035


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()






