
"""simple docstring"""







from __future__ import annotations

from dataclasses import dataclass







@dataclass
class 							__magic_name__     :
					_SCREAMING_SNAKE_CASE       :					float
					_SCREAMING_SNAKE_CASE       :					TreeNode | None     							=   None
					_SCREAMING_SNAKE_CASE       :					TreeNode | None     							=   None




def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE )  ->     bool:







							"""simple docstring"""


							def is_valid_tree(SCREAMING_SNAKE_CASE ) -> bool:
														if node is None:
																					return True

														if not isinstance(SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE ):
																					return False

														try:
																					float(node.data )
														except (TypeError, ValueError):
																					return False

														return is_valid_tree(node.left ) and is_valid_tree(node.right )

							if not is_valid_tree(SCREAMING_SNAKE_CASE ):
														raise ValueError(
														    "Each node should be type of TreeNode and data should be float." )

							def is_binary_search_tree_recursive_check(
							    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE ) -> bool:

														if node is None:
																					return True

														return (
														    left_bound < node.data < right_bound
														    and is_binary_search_tree_recursive_check(node.left							,    SCREAMING_SNAKE_CASE							,    node.data )
														    and is_binary_search_tree_recursive_check(
														        node.right							,    node.data							,    SCREAMING_SNAKE_CASE )
														)

							return is_binary_search_tree_recursive_check(SCREAMING_SNAKE_CASE							,    -float("inf" )							,    float("inf" ) )


if __name__ == "__main__":
		import doctest

		doctest.testmod()


"""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 = 1_00							,    )  ->     float:







							"""simple docstring"""


							__snake_case     			=       x_start
							__snake_case     			=       fnc(SCREAMING_SNAKE_CASE )
							__snake_case     			=       0.0
							for _ in range(SCREAMING_SNAKE_CASE ):
														# Approximates small segments of curve as linear and solve
														# for trapezoidal area
														__snake_case     			=       (x_end - x_start) / steps + xa
														__snake_case     			=       fnc(SCREAMING_SNAKE_CASE )
														area += abs(fxa + fxa ) * (xa - xa) / 2
														# Increment step
														__snake_case     			=       xa
														__snake_case     			=       fxa
							return area


if __name__ == "__main__":
		def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE )  ->     List[Any]:







									"""simple docstring"""


									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:""")
		_SCREAMING_SNAKE_CASE	       =      10
		while i <= 100_000:
				print(F"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
				i *= 10
