Zero Total Charge: How is this Possible?

[fishingspree2]

For a certain problem I have non-zero electrical field E, non-zero electric flux density D, and non-zero volumic charge density ρ_V.

When I integrate pV dV over the given region, I get 0.

How is this possible?

 

[Doc Al]

Why do you think it's not possible to have zero net charge in such a region?