<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def forecast(stl, fc_func, steps=10, seasonal=False, **fc_func_kwargs):
 """Forecast the given decomposition ``stl`` forward by ``steps`` steps using the forecasting function ``fc_func``, optionally including the calculated seasonality. This is an additive model, Y[t] = T[t] + S[t] + e[t] Args: stl (a modified statsmodels.tsa.seasonal.DecomposeResult):
 STL decomposition of observed time series created using the ``stldecompose.decompose()`` method. fc_func (function):
 Function which takes an array of observations and returns a single valued forecast for the next point. steps (int, optional):
 Number of forward steps to include in the forecast seasonal (bool, optional):
 Include seasonal component in forecast fc_func_kwargs: keyword arguments All remaining arguments are passed to the forecasting function ``fc_func`` Returns: forecast_frame (pd.Dataframe):
 A ``pandas.Dataframe`` containing forecast values and a DatetimeIndex matching the observed index. """

    # container for forecast values
    forecast_array = np.array([])

    # forecast trend
    # unpack precalculated trend array stl frame
    trend_array = stl.trend

    # iteratively forecast trend ("seasonally adjusted") component
    # note: this loop can be slow
    for step in range(steps):
        # make this prediction on all available data
        pred = fc_func(np.append(trend_array, forecast_array), **fc_func_kwargs)
        # add this prediction to current array
        forecast_array = np.append(forecast_array, pred)
    col_name = fc_func.__name__

    # forecast start and index are determined by observed data 
    observed_timedelta = stl.observed.index[-1] - stl.observed.index[-2]
    forecast_idx_start = stl.observed.index[-1] + observed_timedelta
    forecast_idx = pd.date_range(start=forecast_idx_start, 
                                 periods=steps,
                                 freq=pd.tseries.frequencies.to_offset(observed_timedelta))

    # (optionally) forecast seasonal & combine 
    if seasonal:
        # track index and value of max correlation
        seasonal_ix = 0
        max_correlation = -np.inf
        # loop over indexes=length of period avgs
        detrended_array = np.asanyarray(stl.observed - stl.trend).squeeze()
        for i, x in enumerate(stl.period_averages):
            # work slices backward from end of detrended observations
            if i == 0:
                # slicing w/ [x:-0] doesn't work
                detrended_slice = detrended_array[-len(stl.period_averages):]        
            else:
                detrended_slice = detrended_array[-(len(stl.period_averages) + i):-i]
            # calculate corr b/w period_avgs and detrend_slice
            this_correlation = np.correlate(detrended_slice, stl.period_averages)[0]
            if this_correlation > max_correlation:
                # update ix and max correlation
                max_correlation = this_correlation
                seasonal_ix = i
        # roll seasonal signal to matching phase
        rolled_period_averages = np.roll(stl.period_averages, -seasonal_ix)
        # tile as many time as needed to reach "steps", then truncate
        tiled_averages = np.tile(rolled_period_averages, 
                                 (steps // len(stl.period_averages) + 1))[:steps]
        # add seasonal values to previous forecast
        forecast_array += tiled_averages                
        col_name += '+seasonal'

    # combine data array with index into named dataframe
    forecast_frame = pd.DataFrame(data=forecast_array, index=forecast_idx)
    forecast_frame.columns = [col_name]  
    return forecast_frame