Convert simulation code to use exact numbers rather than approximation

[gowerc]

The current simulation code essentially performs a rough integration by manually calculating the trapeziums with a user defined spacing between each rectangle. Whilst this works its not that performant and is confusing to explain to end users as they have to define the step size which is something they shouldn't have to worry about. Would be ideal to replace this with using R's numeric integration functions instead. A rough working example of this can be seen below which implements a random sampler for the Weibull distribution:

hazard_fun <- function(t) {
    lambda <- 1 / 200
    gamma <- 0.95
    lambda * gamma * t^(gamma - 1)
}

loss_fun <- function(x, u) {
    survival_prob <- exp(-integrate(hazard_fun, lower = 0, upper = x)$value)
    abs(u - survival_prob)
}

rwei <- function(n) {
    vapply(
        runif(6000),
        \(u) optimise(loss_fun, c(0, 10000), u = u)$minimum,
        numeric(1)
    )
}


## Compare against flexsurv to show that its working
flexsurv::rweibullPH(6000, scale = 1 / 200, shape = 0.95) |>
    density() |>
    plot(col = "red")

rwei(6000) |>
    density() |>
    lines(col = "black")