How to integrate function along circle on sphere?

I need to calculate the mean value of a function along a circle on the surface of a sphere of radius R. The circle is given as the intersection of the sphere and the positive half of a cone of opening half-angle alpha, the axis of which points along (sin A*cos B, sin A*sin B, cos A). The function is given as a function of spherical coordinates f(theta,phi). I have solved the general equation for the intersection of sphere and cone in Cartesian coordinates, so for the points on the circle I know y and z as functions of x and I know the range of x. In other words, I know the x,y,z coordinates of the points on the circle. However, how should I now find the integral of the function over these points? I can't just calculate the function at many points and take the mean as the points won't be spaced evenly if I let x range over the necessary interval. Should I replace theta,phi by their expression in terms of x,y,z and then express y,z as functions of x and integrate with respect to x using something like integral()?

[John D'Errico]

So, you cannot represent the curve parametrically in terms of theta? (From what you have said, you can.) Why cannot you just integrate over this parameter?

[SkyAlliance]

The general equation resulting from intersecting a cone and sphere is rather messy and so are the expressions for y and z as functions of x. I can't really parameterise them in terms of the angle that describes going round the circle (this is not the same as the spherical coordinate theta). I guess since I've got y and z as functions of x, I can use x as my parameter. However, how would I calculate the corresponding line integral in Matlab?