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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 plot_expected_repeat_purchases( model, title="Expected Number of Repeat Purchases per Customer", xlabel="Time Since First Purchase", ax=None, label=None, **kwargs ):
 """ Plot expected repeat purchases on calibration period . Parameters model: lifetimes model A fitted lifetimes model. max_frequency: int, optional The maximum frequency to plot. title: str, optional Figure title xlabel: str, optional Figure xlabel ax: matplotlib.AxesSubplot, optional Using user axes label: str, optional Label for plot. kwargs Passed into the matplotlib.pyplot.plot command. Returns ------- axes: matplotlib.AxesSubplot """

    from matplotlib import pyplot as plt

    if ax is None:
        ax = plt.subplot(111)

    if plt.matplotlib.__version__ >= "1.5":
        color_cycle = ax._get_lines.prop_cycler
        color = coalesce(kwargs.pop("c", None), kwargs.pop("color", None), next(color_cycle)["color"])
    else:
        color_cycle = ax._get_lines.color_cycle
        color = coalesce(kwargs.pop("c", None), kwargs.pop("color", None), next(color_cycle))

    max_T = model.data["T"].max()

    times = np.linspace(0, max_T, 100)
    ax.plot(times, model.expected_number_of_purchases_up_to_time(times), color=color, label=label, **kwargs)

    times = np.linspace(max_T, 1.5 * max_T, 100)
    ax.plot(times, model.expected_number_of_purchases_up_to_time(times), color=color, ls="--", **kwargs)

    plt.title(title)
    plt.xlabel(xlabel)
    plt.legend(loc="lower right")
    return ax