Fuel low warning

What is your question?

The fuel light comes on between 1/2 and 1/4 full. and says I have 6 miles to empty. I can fill up with just a few gals, so I know it is wrong, but I don't know if it will shut down or not. The repair shop cannot do anything about it unless they see it. I cannot get it to the shop at the correct time. Does anyone else have this problem? it is very upsetting.