<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def gaussian_pdf(std=10.0, mean=0.0):
 """Gaussian PDF for orientation averaging. Args: std: The standard deviation in degrees of the Gaussian PDF mean: The mean in degrees of the Gaussian PDF. This should be a number in the interval [0, 180) Returns: pdf(x), a function that returns the value of the spherical Jacobian- normalized Gaussian PDF with the given STD at x (degrees). It is normalized for the interval [0, 180]. """

    norm_const = 1.0
    def pdf(x):
        return norm_const*np.exp(-0.5 * ((x-mean)/std)**2) * \
            np.sin(np.pi/180.0 * x)
    norm_dev = quad(pdf, 0.0, 180.0)[0]
    # ensure that the integral over the distribution equals 1
    norm_const /= norm_dev 
    return pdf