Well, it depends...
A lot of animation software support basic constraints like joint limits or inverse\forward kinematics. These make it easier while your animating the object, but most programs don't actually export the constraints... they turn the animation into keyframes, and export the keyframes. This is actually a very good way to do it, because most of the time all you want in the end is the animation, you don't actually care how it got there, and the keyframes play back much, much, much faster than trying to solve the math.
Physical constraints like you're trying to do generally aren't supported in anything but the very high-end engineering software. Some games also support physical constraints, but generally they use custom level editors to do so. Remember, too, in the end they are solving the constraint by math in the game, just like you are. The constraint that's exported just tells the game what needs solved. So, while a lot of the physics packages will keep you *personally* from having to do the math, the *game* still has to do the math software, so it's still much slower than keyframes animation no matter what you do.
The only advantage you get out of physical constraints is that you can make the animation different every time. That's handy for things like ragdolls, but for something like an engine it probably doesn't make much difference. (You can still alter a keyframe animation in the way you suggest by changing the playback speed.)
I did some googling and it does seem there's a physics package for DarkBasic that supports constraints:
http://darkphysics.thegamecreators.com/
Otherwise, you might want to see what keyframe formats DarkBasic supports.
Another thing to look at are what the X-Plane guys are doing with AC3D. They are basically chaining animations together, and getting some of the effects you're looking for.