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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 paginate(self, model_class, order_by, page_num=1, page_size=100, conditions=None, settings=None):
        '''
        Selects records and returns a single page of model instances.

        - `model_class`: the model class matching the query's table,
          or `None` for getting back instances of an ad-hoc model.
        - `order_by`: columns to use for sorting the query (contents of the ORDER BY clause).
        - `page_num`: the page number (1-based), or -1 to get the last page.
        - `page_size`: number of records to return per page.
        - `conditions`: optional SQL conditions (contents of the WHERE clause).
        - `settings`: query settings to send as HTTP GET parameters

        The result is a namedtuple containing `objects` (list), `number_of_objects`,
        `pages_total`, `number` (of the current page), and `page_size`.
        '''
        count = self.count(model_class, conditions)
        pages_total = int(ceil(count / float(page_size)))
        if page_num == -1:
            page_num = max(pages_total, 1)
        elif page_num < 1:
            raise ValueError('Invalid page number: %d' % page_num)
        offset = (page_num - 1) * page_size
        query = 'SELECT * FROM $table'
        if conditions:
            query += ' WHERE ' + conditions
        query += ' ORDER BY %s' % order_by
        query += ' LIMIT %d, %d' % (offset, page_size)
        query = self._substitute(query, model_class)
        return Page(
            objects=list(self.select(query, model_class, settings)) if count else [],
            number_of_objects=count,
            pages_total=pages_total,
            number=page_num,
            page_size=page_size
        )