  A library of C functions yielding exact solutions of potential and flux
influences due to uniform surface distribution of singularities on flat
triangular and rectangular elements has been developed. This library, ISLES,
has been used to develop the neBEM solver that is both precise and fast in
solving a wide range of problems of scientific and technological interest. Here
we present the exact expressions proposed for computing the influence of
uniform singularity distributions on triangular elements and illustrate their
accuracy. We also present a study concerning the time taken to evaluate these
long and complicated expressions \textit{vis a vis} that spent in carrying out
simple quadratures. Finally, we solve a classic benchmark problem in
electrostatics, namely, estimation of the capacitance of a unit square plate
raised to unit volt. For this problem, we present the estimated values of
capacitance and compare them successfully with some of the most accurate
results available in the literature. In addition, we present the variation of
the charge density close to the corner of the plate for various degrees of
discretization. The variations are found to be smooth and converging. This is
in clear contrast to the criticism commonly leveled against usual BEM solvers.
