Numerical integration library interfacing with eigen

Question

I am looking for a numerical integration library like this one. The examples look very appealing but I see that all test functions use very barebones C arrays.

Do you have any recommendations of libraries for numerical integration over functions of multi-variate arguments that bind easily to Eigen?

I suppose in a pinch, one could always use Eigen's .data() methods and element accessors to emulate the C arrays in their examples.

I just think it would be nice to interface with Eigen in a slightly more streamlined way.

EDIT: To make things more precise consider the following problem:

We have a known function $f(\lambda,a)$ and want to numerically integrate over $\lambda$, where $\lambda \in R^{m}$, so we are looking at a high-dimensional integral and possibly need to use Monte Carlo integration or high-dimensional quadrature methods.

Any leads would be highly appreciated!