The only reliable way to export .max files to any other 3D modeling format is to use the original 3ds Max (previously known as 3D Studio Max) software as the proprietary and closed nature of this format means it is not well-supported in other programs.
Nevertheless, some dedicated 3rd party apps like PolyTrans|CAD+DCC also support formats from 3ds Max so these might potentially help you with max to obj conversion as well. Without either 3ds Max or dedicated (and quite often commercial) conversion software it will be very difficult to convert max to obj.
Updated: June 14, 2023