from scipy.interpolate import interp1d

import numpy as np
x = np.array([0., 1., 3., 4.])
y = np.array([0., 4., 3., 2.])

f = interp1d(x, y)

f(0.5)

f(3.3)

f(np.array([0.5, 1.5, 2.5, 3.5]))

f(-1.)

f = interp1d(x, y, bounds_error=False, fill_value=-10.)

f(-1.0)

f(np.array([-1., 1., 3., 6.]))

f = interp1d(x, y, kind='cubic')
f(0.5)

def simple_function(x):
    return 3. * x**2 + 2. * x + 1.

from scipy.integrate import quad
print(quad(simple_function, 1., 2.))

x = np.linspace(1., 2., 1000)
y = 3. * x**2 + 2. * x + 1.

from scipy.integrate import simps
print(simps(y, x=x))

from scipy.integrate import trapz
print(trapz(y, x=x))


# your solution here



# your solution here



# your solution here