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It is perfectly possible, see for instance this: running a maven scala project. Since Scala compiles to Java bytecode, JVM is not even aware of the underlying implementation language.
In essence after compiling Scala sources using scalac you will get a bunch of .class files which you can later package into a JAR. Then you can simply run them using:
$ java -cp "your.jar:scala-library.jar" com.example.Main
Note that you must include scala-library.jar on the CLASSPATH (currently it is almost 9 MiB...) and specify class containing main method.