Exporting or printing reports containing Mapbox maps within Power BI has always been a challenge in terms of quality and formatting due to the inability of the native export functionality in Power BI. Here are the best practices you can do for exporting with fidelity and high quality:
Optimize Before Export: Always make sure that the Mapbox visuals on your report correspond to the expected resolution and layout for your exports. Use high-contrast color schemes, legible labels, and simplified graphic design in the maps to improve the clarity of exports or prints.
Export as PDF or Image: Do not print directly from Power BI; export your report as a PDF or high-resolution image. For complex visuals such as maps, PDFs tend to preserve the formatting better than actual print. For consistent results, use the "Export to PDF" option from Power BI Desktop or Power BI Service.
Alter Report Layout to Print: If your reports will be commonly printed, design a typical report page just for printing. Make it a static page size instead of dynamic layouts, and move all visuals into the printable area.
Use Screenshot Tools: If the Mapbox map loses quality after exporting, you should capture the visual from Power BI with the highest possible resolution using screenshotting tools. A Snipping Tool or SnagIt and similar tools will do wonders in capturing and saving that map in nice detail.
Try Exporting Different Ways: If none of them work, try exporting the report from both Power BI Desktop and Power BI Service. The rendering and quality might differ somewhat between these environments, so choose the one that gives you the results you want.