





from __future__ import annotations

from collections.abc import Callable


def       UpperCamelCase__(			UpperCamelCase__     :			Callable[[int | float], int | float]					,	UpperCamelCase__     :			int | float					,	UpperCamelCase__     :			int | float					,	UpperCamelCase__     :			int = 1_00					,	)->float:
       A__		   =		x_start
       A__		   =		fnc(UpperCamelCase__    )
       A__		   =		0.0
       for _ in range(UpperCamelCase__    ):
              # Approximates small segments of curve as linear and solve
              # for trapezoidal area
              A__		   =		(x_end - x_start) / steps + xa
              A__		   =		fnc(UpperCamelCase__    )
              area += abs(fxa + fxa    ) * (xa - xa) / 2
              # Increment step
              A__		   =		xa
              A__		   =		fxa
       return area


if __name__ == "__main__":


       def       UpperCamelCase__(			UpperCamelCase__     :			str    )->int:
              return x**3 + x**2

       print('f(x) = x^3 + x^2')
       print('The area between the curve, x = -5, x = 5 and the x axis is:')
       a__: int							   =						10
       while i <= 100_000:
              print(F"with {i} steps: {trapezoidal_area(f, -5, 5, i)}")
              i *= 10












class        SCREAMING_SNAKE_CASE__					:



 def __init__(				self,__lowerCamelCase					):
        A__		   =		size
        A__		   =		[0] * size
        A__		   =		[0] * size



 @staticmethod
 def 							UpperCamelCase     (				__lowerCamelCase					):
        return index | (index + 1)



 @staticmethod
 def 							UpperCamelCase     (				__lowerCamelCase					):
        return (index & (index + 1)) - 1



 def 							UpperCamelCase     (				self,__lowerCamelCase,__lowerCamelCase					):
        A__		   =		value
        while index < self.size:
               A__		   =		self.get_prev(__lowerCamelCase					) + 1
               if current_left_border == index:
                      A__		   =		value
               else:
                      A__		   =		max(__lowerCamelCase,__lowerCamelCase,__lowerCamelCase					)
               A__		   =		self.get_next(__lowerCamelCase					)




 def 							UpperCamelCase     (				self,__lowerCamelCase,__lowerCamelCase					):
        right -= 1  # Because of right is exclusive
        A__		   =		0
        while left <= right:
               A__		   =		self.get_prev(__lowerCamelCase					)
               if left <= current_left:
                      A__		   =		max(__lowerCamelCase,self.tree[right]					)
                      A__		   =		current_left
               else:
                      A__		   =		max(__lowerCamelCase,self.arr[right]					)
                      right -= 1
        return result


if __name__ == "__main__":
       import doctest

       doctest.testmod()





