[Dan Zollman]

I'm pretty sure that f(x) = tan^-1(d/x) would work.

If you draw lines through the front and back wheels (basically, through their axles) as TimCraig said, I am assuming that the intersection of those lines would be the center point of the arc. The line from the point between the two back wheels to the point between the front wheels gives you d (I'll call it line D). Line D is perpendicular to the line drawn from the back wheels to the center of the circle/arc (line B). Thus lines D and B make a right triangle with hypotenuse drawn from the front wheels to the center of the circle.

The tangent function is described as the ratio of length d to length b. b is the arc radius. Angle A is the angle between b and the hypotenuse.
tan(A) = d/x
A = tan^-1(d/x)

I don't think it matters if the front wheels don't share an axle, because the lines are drawn from the midpoint between the two wheels.