



"""simple docstring"""


from __future__ import annotations

from collections.abc import Callable

snake_case_    					=	list[list[float | int]]

def 			_lowerCAmelCase				(       lowercase_		,     lowercase_						):
						UpperCAmelCase					=			len(lowercase_						)
						UpperCAmelCase					=			[[0 for _ in range(size + 1						)] for _ in range(lowercase_						)]
						UpperCAmelCase					=			42
						UpperCAmelCase					=			42
						UpperCAmelCase					=			42
						UpperCAmelCase					=			42
						UpperCAmelCase					=			42
						UpperCAmelCase					=			42

						for row in range(lowercase_						):
												for col in range(lowercase_						):
																		UpperCAmelCase					=			matrix[row][col]

												UpperCAmelCase					=			vector[row][0]

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

												for rowa in range(row + 1		,     lowercase_						):
																		UpperCAmelCase					=			augmented[rowa][col] / augmented[row][col]
																		UpperCAmelCase					=			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_						):
																		UpperCAmelCase					=			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 			_lowerCAmelCase				(       lowercase_						):
						UpperCAmelCase					=			len(lowercase_						)
						UpperCAmelCase					=			[[0 for _ in range(lowercase_						)] for _ in range(lowercase_						)]
						UpperCAmelCase					=			[[0] for _ in range(lowercase_						)]
						UpperCAmelCase					=			42
						UpperCAmelCase					=			42
						UpperCAmelCase					=			42
						UpperCAmelCase					=			42

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

						UpperCAmelCase					=			solve(lowercase_		,     lowercase_						)

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

						return interpolated_func

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

def 			_lowerCAmelCase				(       lowercase_ = question_function		,     lowercase_ = 10						):
						UpperCAmelCase					=			[func(lowercase_						) for x_val in range(1		,     order + 1						)]

						UpperCAmelCase					=			[
						    interpolate(data_points[:max_coeff]						) for max_coeff in range(1		,     order + 1						)
						]

						UpperCAmelCase					=			0
						UpperCAmelCase					=			42
						UpperCAmelCase					=			42

						for poly in polynomials:
												UpperCAmelCase					=			1
												while func(lowercase_						) == poly(lowercase_						):
																		x_val += 1

												ret += poly(lowercase_						)

						return ret


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









"""simple docstring"""


from math import factorial, radians

def 			_lowerCAmelCase				(       lowercase_		,     lowercase_ = 18		,     lowercase_ = 10						):
						UpperCAmelCase					=			angle_in_degrees - ((angle_in_degrees // 3_6_0.0) * 3_6_0.0)

						# Converting from degrees to radians
						UpperCAmelCase					=			radians(lowercase_						)

						UpperCAmelCase					=			angle_in_radians
						UpperCAmelCase					=			3
						UpperCAmelCase					=			-1

						for _ in range(lowercase_						):
												result += (b * (angle_in_radians**a)) / factorial(lowercase_						)

												UpperCAmelCase					=			-b  # One positive term and the next will be negative and so on...
												a += 2  # Increased by 2 for every term.

						return round(lowercase_		,     lowercase_						)


if __name__ == "__main__":
				__import__("""doctest""").testmod()





