Passing environments: why doesn't this work???

This is a trivial example I set up to see if I could pass an environment and
use the variables in it
(this is for a function that will be called many times and might need to use
a lot of variables that
won't be changing, so it seemed more sensible to use an environment).

Here's the code:
#########################
#The outer function
run.internal.env <- function(x) {
 in.env <- new.env()
 assign('x', x, envir=in.env)
 print(eval(x^2, envir=in.env))
 print(ls(envir=in.env))
 return(use.internal.env(in.env))
 }

#The inner function
use.internal.env <- function(env) {
 print(ls(envir=env))
 return(eval(x^2, envir=env))
 }
##########################
Now if I type

run.internal.env(2), my output looks like

[1] 4        [This is the evaluation in the outer routine]
[1] "x"      [This is the "ls" from the outer routine]
[1] "x"      [This is the "ls" from the inner routine]
Error in eval(x^2, envir=env): object "x" not found   [??? It was listed, so
why can't it be evaluated???]

If there's anything called "x" in the global environment, it will evaluate
that x^2 instead, e.g.
x <- 1:3
run.internal.env(2)
[1] 4        [This is the evaluation in the outer routine]
[1] "x"      [This is the "ls" from the outer routine]
[1] "x"      [This is the "ls" from the inner routine]
[1] 1 4 9

Is there any way to force it to use the environment I actually want, and
keep all the values I assigned in there?

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