<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def _request(self, lat_min, lon_min, lat_max, lon_max, start, end, picture_size=None, set_=None, map_filter=None):
 """ Internal method to send requests to the Panoramio data API. :param lat_min: Minimum latitude of the bounding box :type lat_min: float :param lon_min: Minimum longitude of the bounding box :type lon_min: float :param lat_max: Maximum latitude of the bounding box :type lat_max: float :param lon_max: Maximum longitude of the bounding box :type lon_max: float :param start: Start number of the number of photo's to retrieve, where 0 is the most popular picture :type start: int :param end: Last number of the number of photo's to retrieve, where 0 is the most popular picture :type end: int :param picture_size: This can be: original, medium (*default*), small, thumbnail, square, mini_square :type picture_size: basestring :param set_: This can be: public, popular or user-id; where user-id is the specific id of a user (as integer) :type set_: basestring/int :param map_filter: Whether to return photos that look better together; when True, tries to avoid returning photos of the same location :type map_filter: bool :return: JSON response of the request formatted as a dictionary. """

        if not isinstance(lat_min, float):
            raise PynoramioException(
                '{0}._request requires the lat_min parameter to be a float.'.format(self.__class__.__name__))
        if not isinstance(lon_min, float):
            raise PynoramioException(
                '{0}._request requires the lon_min parameter to be a float.'.format(self.__class__.__name__))
        if not isinstance(lat_max, float):
            raise PynoramioException(
                '{0}._request requires the lat_max parameter to be a float.'.format(self.__class__.__name__))
        if not isinstance(lon_max, float):
            raise PynoramioException(
                '{0}._request requires the lon_max parameter to be a float.'.format(self.__class__.__name__))

        if not isinstance(start, int):
            raise PynoramioException(
                '{0}._request requires the start parameter to be an int.'.format(self.__class__.__name__))
        if not isinstance(end, int):
            raise PynoramioException(
                '{0}._request requires the end parameter to be an int.'.format(self.__class__.__name__))

        url = self.base_url + '&minx={0}&miny={1}&maxx={2}&maxy={3}&from={4}&to={5}'.format(lon_min, lat_min,
                                                                                            lon_max, lat_max,
                                                                                            start, end)

        if picture_size is not None and isinstance(picture_size, basestring) \
                and picture_size in ['original', 'medium', 'small', 'thumbnail', 'square', 'mini_square']:
            url += '&size={0}'.format(picture_size)

        if set_ is not None and (isinstance(set_, basestring) and set_ in ['public', 'full']) \
                or (isinstance(set_, int)):
            url += '&set={0}'.format(set_)
        else:
            url += '&set=public'

        if map_filter is not None and isinstance(map_filter, bool) and not map_filter:
            url += '&map_filter=false'

        r = requests.get(url)
        try:
            return r.json()
        except ValueError:
            # add your debugging lines here, for example, print(r.url)
            raise PynoramioException(
                'An invalid or malformed url was passed to {0}._request'.format(self.__class__.__name__))