Mikita rbc310 string trimmer will not run at high rpms?

Sounds like you have dirt/debris in your carburetor jets,fuel passages or a diaphgram that is becoming non-flexible.
Be sure to check your fuel tank for water and dirt/debris, if there is water/debris then you need to clean your tank.
Also check you fuel line condition after a while they will degrade and need replacment.
Make sure you are getting spark at the spark plug, to do this:
Remove your spark plug and check to be sure you are getting fire at the spark plug.
You do this by grounding the plug on the head of the engine and pulling the crank rope, if you are getting spark then:
Check/Clean/Replace your fuel filter if you have one, normally they are located in the fuel tank of weedeaters.
When you remove your fuel lines from the carburetor be sure to make a drawing to how the lines are connected to the carburetor.
Normally the big line will be the line the fuel filter is connected to inside of the tank.The smaller of the two lines is the return to the fuel tank from the carburetor after it is pumped thru the carburetor by the primer bulb.
Also make sure you are using fresh fuel...and oil mix if your using a two cycle mower or weedeater with the oil to the right mixture and not too much oil as it can cause hard starting.
If the mower/weedeater is over a couple of years old, then I recommend that you buy and install a new carburetor repair kit,because the diaphragm will get hard and that will cause it to be hard to crank.
Sounds like you will need to clean the carburetor or replace your carburetor internal rubber parts like the diaphgram and O rings.
I recommend that you use a laquer thinner type cleaner to clean and dissolve the laquer build-up in the float and needle jet passages.
Be sure to remove all plastic and rubber parts before using the laquer thinner because it can dissolve the plastic parts and render them unuseable.
Be sure to use compressed air to blow out all the fuel and air passages.
Be careful when blowing out the passages, because there are sometimes small rubber type seats in the bottom of some of the passages.
Sometimes you can get by with priming the carburetor or using starting fluid and letting it run a few times like that and it will flush the gunk out of the jets,but most of the time you will need to rebuild the carburetor.
Keep in mind that the float (if you have one) for the carburetor must be level when you go to reassemble the carburetor or follow the instructions you get with the carburetor kit.
When you clean your carburetor and remove the jet screws, you will first need to lightly seat the jet screws.
But before you lightly seat the jet screws count the number of turns it takes to seat the jet screws from their original position.
Be sure to mark the turns down on a piece of paper.
That way when you put the jets back in, you know to lightly seat them first and then turn them back out to their orginal position before you started.
Once you have your carburetor rebuilt that should solve your problem.