d01ah computes a definite integral over a finite range to a specified relative accuracy using a method described by Patterson.

d01aj is a general purpose integrator which calculates an approximation to the integral of a function $f\left(x\right)$ over a finite interval $\left[a,b\right]$:

d01ak is an adaptive integrator, especially suited to oscillating, nonsingular integrands, which calculates an approximation to the integral of a function $f\left(x\right)$ over a finite interval $\left[a,b\right]$:

d01al is a general purpose integrator which calculates an approximation to the integral of a function $f\left(x\right)$ over a finite interval $\left[a,b\right]$: where the integrand may have local singular behaviour at a finite number of points within the integration interval.

d01am calculates an approximation to the integral of a function $f\left(x\right)$ over an infinite or semi-infinite interval $\left[a,b\right]$:

d01an calculates an approximation to the sine or the cosine transform of a function $g$ over $\left[a,b\right]$: (for a user-specified value of $\omega$).

d01ap is an adaptive integrator which calculates an approximation to the integral of a function $g\left(x\right)w\left(x\right)$ over a finite interval $\left[a,b\right]$: where the weight function $w$ has end point singularities of algebraico-logarithmic type.

d01aq calculates an approximation to the Hilbert transform of a function $g\left(x\right)$ over $\left[a,b\right]$: for user-specified values of $a$, $b$ and $c$.

d01ar computes definite and indefinite integrals over a finite range to a specified relative or absolute accuracy, using the method described in Patterson (1968).

d01as calculates an approximation to the sine or the cosine transform of a function $g$ over $\left[a,\infty \right)$: (for a user-specified value of $\omega$).

d01bc returns the weights (normal or adjusted) and abscissae for a Gaussian integration rule with a specified number of abscissae. Six different types of Gauss rule are allowed.

d01bd calculates an approximation to the integral of a function over a finite interval $\left[a,b\right]$: It is non-adaptive and as such is recommended for the integration of ‘smooth’ functions. These exclude integrands with singularities, derivative singularities or high peaks on $\left[a,b\right]$, or which oscillate too strongly on $\left[a,b\right]$.

d01da attempts to evaluate a double integral to a specified absolute accuracy by repeated applications of the method described by Patterson (1968) and Patterson (1969).

d01fc attempts to evaluate a multidimensional integral (up to $15$ dimensions), with constant and finite limits, to a specified relative accuracy, using an adaptive subdivision strategy.

d01gd calculates an approximation to a definite integral in up to $20$ dimensions, using the Korobov–Conroy number theoretic method. This method is designed to be particularly efficient on vector processors.

d01gy calculates the optimal coefficients for use by (D01GCF not in this release) d01gd, for prime numbers of points.

d01gz calculates the optimal coefficients for use by (D01GCF not in this release) d01gd, when the number of points is the product of two primes.

d01ja attempts to evaluate an integral over an $n$-dimensional sphere ($n=2$, $3$, or $4$), to a user-specified absolute or relative accuracy, by means of a modified Sag–Szekeres method. The method can handle singularities on the surface or at the centre of the sphere, and returns an error estimate.

d01pa returns a sequence of approximations to the integral of a function over a multidimensional simplex, together with an error estimate for the last approximation.