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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def profile_slope(self, kwargs_lens_list, lens_model_internal_bool=None, num_points=10):
 """ computes the logarithmic power-law slope of a profile :param kwargs_lens_list: lens model keyword argument list :param lens_model_internal_bool: bool list, indicate which part of the model to consider :param num_points: number of estimates around the Einstein radius :return: """

        theta_E = self.effective_einstein_radius(kwargs_lens_list)
        x0 = kwargs_lens_list[0]['center_x']
        y0 = kwargs_lens_list[0]['center_y']
        x, y = util.points_on_circle(theta_E, num_points)
        dr = 0.01
        x_dr, y_dr = util.points_on_circle(theta_E + dr, num_points)
        if lens_model_internal_bool is None:
            lens_model_internal_bool = [True]*len(kwargs_lens_list)

        alpha_E_x_i, alpha_E_y_i = self._lensModel.alpha(x0 + x, y0 + y, kwargs_lens_list, k=lens_model_internal_bool)
        alpha_E_r = np.sqrt(alpha_E_x_i**2 + alpha_E_y_i**2)
        alpha_E_dr_x_i, alpha_E_dr_y_i = self._lensModel.alpha(x0 + x_dr, y0 + y_dr, kwargs_lens_list,
                                                               k=lens_model_internal_bool)
        alpha_E_dr = np.sqrt(alpha_E_dr_x_i ** 2 + alpha_E_dr_y_i ** 2)
        slope = np.mean(np.log(alpha_E_dr / alpha_E_r) / np.log((theta_E + dr) / theta_E))
        gamma = -slope + 2
        return gamma