docker container exits out immediately with a script attached

I’m going to recommend an extremely different workflow from what you suggest. Rather than manually installing software and trying to type arguments into the stdin of a shell script, you can build this into a reusable Docker image and provide its options as environment variables.

In comments you describe a workflow where you first start a container, then get a debugging shell inside of it, and then install curl. Unless you’re really truly debugging, this is a pretty unusual workflow: anything you install this way will get lost as soon as the container exits, and you’ll have to repeat this step every time you re-run the container. Instead, create a new empty directory, and inside that create a file named Dockerfile (exactly that name, no extension, capital D) containing

# Start our new image from this base
FROM ubuntu

# Install any OS-level packages we need
RUN apt-get update 
 && DEBIAN_FRONTEND=noninteractive   # avoid post-installation questions
    apt-get install 
      --no-install-recommends        # don't install unneeded extra packages
      --assume-yes                   # (-y) skip an "are you sure" prompt
      curl

Rather than try to read from the container’s input, you can take the URL as an environment variable. In most cases the best way to give the main command to a container is by specifying it in the Dockerfile. You can imagine running a larger script or program here as well, and it would take the some environment-variable setting (using Python’s os.environ, Node’s process.env, Ruby’s ENV, etc.).

In our case, let’s make the main container command be the single curl command that you’re trying to run. We haven’t specified the value of the environment variable yet, and that’s okay: this shell command isn’t evaluated until the container actually runs.

# at the end of the Dockerfile
CMD curl "$website"

Now let’s build and run it. When we do launch the container, we need to provide that $website environment variable value, which we can do with a docker run -e option.

# Build the image:
docker build 
  -t my/curl  # giving it a name
  .           # using the content in the current directory

docker run 
  --rm        # deleting the container when done
  -e website=https://stackoverflow.com 
  my/curl     # with the same name as above

So note that we’re starting the container in the foreground (no -d option) since we want to see its output and we expect it to exit promptly; we’re cleaning up the container when it’s done; we’re not trying to pass a full shell script as a command-line argument; and we are providing our options on the command line, so we don’t need to make the container’s stdin work (no -i or -t option).

A Docker container is a wrapper around a single process. When that process exits, the container exits too. In this example, the thing you want the container to do is run a curl command; that’s not a long-running process, hence docker run --rm but not -d. There’s not an "afterwards" here, if you need to query a different Web site then launch a new container. It’s very normal to destroy and recreate containers, especially since there are many options that can only be specified when you first start a container.

With the image and container we’ve built here, in fact, it’s useful to think about them as analogous to the /usr/bin/curl binary on your host. You build it once into a reusable artifact (here the Docker image), and you run multiple instances of it (curl commands or new Docker containers) giving options on the command line at startup time. You do not typically "get a shell" inside a curl command-line invocation, and I’d similarly avoid docker exec outside of debugging tasks.