Only by creating your own map tiles, see recent postings on that subject.

What you are seeing is not the map, but rendered bit map images derived from the map. In the case of the standard rendering, all except the highest zoom level are pre-computed. for the other options, they are probably all pre-computed.

The name of the tile includes the zoom level, and the corner coordinates, and you can only request tiles that match the coordinates and zoom levels known to the system.

There is an option to export PDF, which will give you a scalable image, but the zoom levels still determine whether or not features are included. I think the PDFs are all generated on the fly.

Also note that the rendered maps are there to help mappers and as proofs of concept. OSM does not have the resources or funding to support end user map services similar to Google or Bing.