> polyroot(c(40,0,0,5,20,10))
[1]  0.7747767+0.7263645i -0.7747767+1.0830293i -0.7747767-1.0830293i
[4]  0.7747767-0.7263645i -2.0000000+0.0000000i
> 

install.packages("cubature")
library(cubature)

> testFn0 <- function(x) {
+   prod(cos(x))
+ }
> 
> adaptIntegrate(testFn0, rep(0,2), rep(1,2), tol=1e-4)
$integral
[1] 0.7080734

$error
[1] 1.709434e-05

$functionEvaluations
[1] 17

$returnCode
[1] 0



> M_2_SQRTPI <- 2/sqrt(pi)
> testFn1 <- function(x) {
+   scale = 1.0
+   val = 0
+   dim = length(x)
+   val = sum (((1-x) / x)^2)
+   scale = prod(M_2_SQRTPI/x^2)
+   exp(-val) * scale
+ }
> 
> adaptIntegrate(testFn1, rep(0, 3), rep(1, 3), tol=1e-4)
$integral
[1] 1.00001

$error
[1] 9.677977e-05

$functionEvaluations
[1] 5115

$returnCode
[1] 0




> testFn2 <- function(x) {
+   ## discontinuous objective: volume of hypersphere
+   radius = as.double(0.50124145262344534123412)
+   ifelse(sum(x*x) < radius*radius, 1, 0)
+ }
> 
> adaptIntegrate(testFn2, rep(0, 2), rep(1, 2), tol=1e-4)
$integral
[1] 0.19728

$error
[1] 1.972614e-05

$functionEvaluations
[1] 166141

$returnCode
[1] 0