Java and AppleScript's "call method"

As I ask this question, I’m imagining whistling wind and rolling tumbleweeds when I consider the likelyhood of a response, but still, I strive on with meager hope…

I’d like to have a Java application execute an AppleScript (that much I’ve managed to do using NSAppleScript and simple scripts), but… here’s the tricky part… I’d like the AppleScript, while running, to be able to call methods in my Java program, for both passing information and for doing things that are much easier to do in Java than in AppleScript.

Let’s start with a contrived example, and proceed to make it even more contrived:

public void test()
{
  String                script = "set a to 2n" +
                                 "set b to 3n" +
                                 "set c to a + b";
  NSAppleScript         aScript = new NSAppleScript(script);
  NSMutableDictionary   errors = new NSMutableDictionary();
  System.out.println(aScript.execute(errors).stringValue());
}

The above works, and prints the number 5.

Suppose, however, I wanted to do the addition via a Java method called addEmUp():

public double addEmUp(double a, double b)
{
  return a + b;
}

public void test()
{
  String                script = "set a to 2n" +
                                 "set b to 3n" +
                                 "set c to call method "addEmUp:" of (class? object?) SomethingGoesHere " +
                                   "with parameters {a, b}";
  NSAppleScript         aScript = new NSAppleScript(script);
  NSMutableDictionary   errors = new NSMutableDictionary();
  System.out.println(aScript.execute(errors).stringValue());
}

What sort of wrapped or glue do I need to make addEmUp accessible this way? How to I pass and retrieve values? (For instance, I doubt passing and return doubles directly works as I’ve shown, and I don’t if “set c to result of call method” works or even makes sense.

Hopefully someone out there will understand what I’m getting at an maybe even have (gasp!) an answer. I’d be most appreciative.