diff --git a/ibis/backends/trino/__init__.py b/ibis/backends/trino/__init__.py
index cd0938efe853..e2654f488e01 100644
--- a/ibis/backends/trino/__init__.py
+++ b/ibis/backends/trino/__init__.py
@@ -6,12 +6,12 @@
 from functools import cached_property
 from operator import itemgetter
 from typing import TYPE_CHECKING, Any
-from urllib.parse import unquote_plus, urlparse
+from urllib.parse import unquote_plus
 
 import sqlglot as sg
 import sqlglot.expressions as sge
 import trino
-from trino.auth import BasicAuthentication
+from trino.auth import Authentication, BasicAuthentication
 
 import ibis
 import ibis.backends.sql.compilers as sc
@@ -60,7 +60,10 @@ def _from_url(self, url: ParseResult, **kwarg_overrides):
         if url.password:
             kwargs["auth"] = unquote_plus(url.password)
         if url.hostname:
-            kwargs["host"] = url.hostname
+            # Do NOT convert to url.hostname, the trino client expects an entire URL
+            # to do inference on http vs https, port, etc.
+            # https://github.com/trinodb/trino-python-client/blob/2108c38dea79518ffb74370177df2dc95f1e6d96/trino/dbapi.py#L169
+            kwargs["host"] = url
         if database:
             kwargs["database"] = database
         if url.port:
@@ -245,11 +248,12 @@ def list_tables(
     def do_connect(
         self,
         user: str = "user",
-        auth: str | None = None,
+        auth: str | Authentication | None = None,
         host: str = "localhost",
         port: int = 8080,
         database: str | None = None,
         schema: str | None = None,
+        *,
         source: str | None = None,
         timezone: str = "UTC",
         **kwargs,
@@ -261,7 +265,7 @@ def do_connect(
         user
             Username to connect with
         auth
-            Authentication method or password to use for the connection.
+            Password or authentication method to use for the connection.
         host
             Hostname of the Trino server
         port
@@ -296,11 +300,7 @@ def do_connect(
         >>> con = ibis.trino.connect(database=catalog, schema=schema)
         >>> con = ibis.trino.connect(database=catalog, schema=schema, source="my-app")
         """
-        if (
-            isinstance(auth, str)
-            and (scheme := urlparse(host).scheme)
-            and scheme != "http"
-        ):
+        if isinstance(auth, str):
             auth = BasicAuthentication(user, auth)
 
         self.con = trino.dbapi.connect(
diff --git a/ibis/backends/trino/tests/test_client.py b/ibis/backends/trino/tests/test_client.py
index 08a03ec6a9f7..7d1fbae64806 100644
--- a/ibis/backends/trino/tests/test_client.py
+++ b/ibis/backends/trino/tests/test_client.py
@@ -68,6 +68,37 @@ def test_list_databases(con):
     assert {"information_schema", "sf1"}.issubset(con.list_databases(catalog="tpch"))
 
 
+@pytest.mark.parametrize("auth_type", ["str", "obj"])
+@pytest.mark.parametrize(("http_scheme"), ["http", "https", None])
+def test_con_auth_str(http_scheme, auth_type):
+    """If a non-str object is given to auth, it should be used as is, no matter what.
+    If a str is given to auth, it should be converted to a BasicAuthentication.
+    This happens no matter the http_scheme given.
+
+    Tests for
+    https://github.com/ibis-project/ibis/issues/9113
+    https://github.com/ibis-project/ibis/issues/9956
+    https://github.com/ibis-project/ibis/issues/11841
+    """
+    from trino.auth import BasicAuthentication
+
+    if auth_type == "str":
+        auth = TRINO_PASS
+    else:
+        auth = BasicAuthentication(TRINO_USER, TRINO_PASS)
+
+    con = ibis.trino.connect(
+        user=TRINO_USER,
+        host=TRINO_HOST,
+        port=TRINO_PORT,
+        auth=auth,
+        database="hive",
+        schema="default",
+        http_scheme=http_scheme,
+    )
+    assert con.con.auth == BasicAuthentication(TRINO_USER, TRINO_PASS)
+
+
 @pytest.mark.parametrize(("source", "expected"), [(None, "ibis"), ("foo", "foo")])
 def test_con_source(source, expected):
     con = ibis.trino.connect(