Can we solve for lambda in R? Assuming a poisson distribution, is there a way to solve for lambda in R?
My inputs would be "x", and Pr(X<=x) ... and I would like R to tell me the lambda.
Thanks

As noted by @whuber in the comments, if the task is to find $\lambda$ for a given value of $P(X\le x)$ assuming that $X\sim \operatorname{Poisson}(\lambda)$ this can be computed via the built-in gamma distribution quantile function (the inverse of the cdf) as follows.
Note first that $X$ can be seen as then number of occurrences on the interval $(0,1]$ in a Poisson process with intensity $\lambda$.  The event $X\le x$ is then equivalent to the event that the $(x+1)$'th gamma distributed arrival time $T_{x+1}>1$.  Hence,
$$
P(X\le x)=P(T_{x+1}>1)=1-F_{\lambda,x+1}(1) \tag{1}
$$
where $F_{\lambda,\alpha}$ is the cdf of the gamma distribution with rate parameter $\lambda$ and shape parameter $\alpha$.
In general the cdfs of gamma distributions with rate parameters $\lambda$ and 1 are related via
$$
F_{\lambda,\alpha}(t)=F_{1,\alpha}(\lambda t). \tag{2}
$$
Hence, combining (1) and (2), and solving for $\lambda$ we obtain
$$
\lambda = F_{1,x+1}^{-1}(1-P(X\le x))
$$
that is, qgamma(1 - 0.8666283, rate = 1, shape = 7 + 1) given that $x=7$ and $P(X\le x)=0.8666283$.
