LastCalc's parser is very sophisticated and has many components, but fortunately SequentialParser.java provides a very friendly high-level interface to it, which is used at various points through LastCalc's user-facing code.
Here is a simple usage example:
finalSequentialParser sp =SequentialParser.create();
finalTokenList res = sp.parseNext("a+1");
This will print "53".
You can see many other usage examples in SequentialParserTest.java - which also serves as a suite of integration tests for all of LastCalc's parsing code.