import math
import plotly.graph_objects as go
import numpy as np


def regions(K, x):
    if x < 0:
        return math.e ** ((100 - K**2) ** 0.5) * x
    elif 0 < x < 1:
        return (math.cos(K * x)) + (math.sqrt(100 - K**2) / K) * math.sin(K * x)
    else:
        return K

if __name__ == "__main__":
    # Generates an array of 100 x values between -2 and 2
    x = np.linspace(-2, 2, 100)
    
    # Allows us to evaluate the regions function over the whole range of x values
    regionsVec = np.vectorize(regions)
    
    # Apply the regions function to the range.
    # I assume K is a constant. Using 9.9 for illustration purposes.
    y = regionsVec(9.9, x)
    
    # Make a graph with plotly
    fig = go.Figure(data=go.Scatter(x=x, y=y, mode="lines"))
    fig.show()