Modern constraint answer set solving Answer Set Programming (ASP) is a declarative problem solving approach combining a rich yet simple modeling language with high performance solving capabilities. Although this has already resulted in various applications certain aspects of such applications are more naturally modeled using variables over finite domains for accounting for resources fine timings coordinates or functions. Our goal is thus to extend ASP with constraints over integers while preserving its declarative nature. This allows for fast prototyping and elaboration tolerant problem descriptions of resource related applications. The resulting paradigm is called Constraint Answer Set Programming (CASP). We present three different approaches for solving CASP problems. The first one a lazy modular approach combines an ASP solver with an external system for handling constraints. This approach has the advantage that two state of the art technologies work hand in hand to solve the problem each concentrating on its part of the problem. The drawback is that ...