

def 		UpperCamelCase      (lowercase_:				float					,   lowercase_:				float      )  ->   float:

	if density <= 0:
		raise ValueError("""Impossible fluid density"""      )
	if bulk_modulus <= 0:
		raise ValueError("""Impossible bulk modulus"""      )

	return (bulk_modulus / density) ** 0.5


if __name__ == "__main__":
	import doctest

	doctest.testmod()






from __future__ import annotations

from collections.abc import Callable

A_ :				List[Any]						 =    list[list[float | int]]

def 		UpperCamelCase      (lowercase_:				Matrix					,   lowercase_:				Matrix      )  ->   Matrix:
	A__							:					int       =	len(lowercase_      )
	A__							:					Matrix       =	[[0 for _ in range(size + 1      )] for _ in range(lowercase_      )]
	A__							:					int
	A__							:					int
	A__							:					int
	A__							:					int
	A__							:					int
	A__							:					float

	for row in range(lowercase_      ):
		for col in range(lowercase_      ):
			A__							:					List[str]       =	matrix[row][col]

		A__							:					int       =	vector[row][0]

	A__							:					Optional[int]       =	0
	A__							:					str       =	0
	while row < size and col < size:
		# pivoting
		A__							:					int       =	max((abs(augmented[rowa][col]      ), rowa) for rowa in range(lowercase_					,   lowercase_      )      )[
		    1
		]
		if augmented[pivot_row][col] == 0:
			col += 1
			continue
		else:
			A__     ,     A__							:					Union[str, Any]       =	augmented[pivot_row], augmented[row]

		for rowa in range(row + 1					,   lowercase_      ):
			A__							:					List[Any]       =	augmented[rowa][col] / augmented[row][col]
			A__							:					Dict       =	0
			for cola in range(col + 1					,   size + 1      ):
				augmented[rowa][cola] -= augmented[row][cola] * ratio

		row += 1
		col += 1

	# back substitution
	for col in range(1					,   lowercase_      ):
		for row in range(lowercase_      ):
			A__							:					List[str]       =	augmented[row][col] / augmented[col][col]
			for cola in range(lowercase_					,   size + 1      ):
				augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
	return [
	    [round(augmented[row][size] / augmented[row][row]					,   10      )] for row in range(lowercase_      )
	]

def 		UpperCamelCase      (lowercase_:				list[int]      )  ->   Callable[[int], int]:
	A__							:					int       =	len(lowercase_      )
	A__							:					Matrix       =	[[0 for _ in range(lowercase_      )] for _ in range(lowercase_      )]
	A__							:					Matrix       =	[[0] for _ in range(lowercase_      )]
	A__							:					Matrix
	A__							:					int
	A__							:					int
	A__							:					int

	for x_val, y_val in enumerate(lowercase_      ):
		for col in range(lowercase_      ):
			A__							:					Dict       =	(x_val + 1) ** (size - col - 1)
		A__							:					Any       =	y_val

	A__							:					Union[str, Any]       =	solve(lowercase_					,   lowercase_      )

	def interpolated_func(lowercase_:				int      ) -> int:
		return sum(
		    round(coeffs[x_val][0]      ) * (var ** (size - x_val - 1))
		    for x_val in range(lowercase_      )      )

	return interpolated_func

def 		UpperCamelCase      (lowercase_:				int      )  ->   int:
	return (
	    1
	    - variable
	    + variable**2
	    - variable**3
	    + variable**4
	    - variable**5
	    + variable**6
	    - variable**7
	    + variable**8
	    - variable**9
	    + variable**10
	)

def 		UpperCamelCase      (lowercase_:				Callable[[int], int] = question_function					,   lowercase_:				int = 10      )  ->   int:
	A__							:					list[int]       =	[func(lowercase_      ) for x_val in range(1					,   order + 1      )]

	A__							:					list[Callable[[int], int]]       =	[
	    interpolate(data_points[:max_coeff]      ) for max_coeff in range(1					,   order + 1      )
	]

	A__							:					int       =	0
	A__							:					Callable[[int], int]
	A__							:					int

	for poly in polynomials:
		A__							:					List[str]       =	1
		while func(lowercase_      ) == poly(lowercase_      ):
			x_val += 1

		ret += poly(lowercase_      )

	return ret


if __name__ == "__main__":
	print(f'''{solution() = }''')



