Dart, how to parse user string into functional dart code?
There is no notion of eval in Dart, and it is not possible to dynamically build code. You can run code in a different isolate using spawnUri (see http://api.dartlang.org/docs/releases/latest/dart_isolate.html). When not running in the Dartium browser, note that the Dart code needs to be compiled to JavaScript using dart2js. The site http://try.dartlang.org/ does all that.
Some time in the future Dart might get mirror builders which can be used for "programs to extend and modify themselves" (citation from last paragraph in https://www.dartlang.org/articles/reflection-with-mirrors/).