diff --git a/examples/demo_theory_functionality.ipynb b/examples/demo_theory_functionality.ipynb
index 81b244d38..cda9a8e7c 100644
--- a/examples/demo_theory_functionality.ipynb
+++ b/examples/demo_theory_functionality.ipynb
@@ -348,7 +348,9 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "metadata": {},
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [],
    "source": [
     "plot_profile(r3d, kappa, \"$\\\\kappa$\")"
@@ -437,7 +439,7 @@
     "- In CCL, the default Einasto slope depends on cosmology, redshift and halo mass. \n",
     "- In NumCosmo, the default value is $\\alpha_{\\rm ein}=0.25$.\n",
     "\n",
-    "**NB: for CCL, setting a user-defined value for the Einasto slope is only available for CCL version >= 2.6.** Earlier versions only allow the default option.\n",
+    "**NB: for CCL, setting a user-defined value for the Einasto slope is only available for versions >= 2.6.** Earlier versions only allow the default option.\n",
     "\n",
     "The verbose option allows to print the value of $\\alpha$ that is being used, as follows:"
    ]
@@ -459,8 +461,8 @@
     "    verbose=True,\n",
     ")\n",
     "\n",
-    "# For CCL < 2.6, the above call will return an error, as alpha_ein could not be set. The call below, not specifying alpha_ein,\n",
-    "# will use the default value (for both backend)\n",
+    "# For CCL < 2.6, the above call will return an error, as alpha_ein cannot not be set. The call below, not specifying alpha_ein,\n",
+    "# will use the default value (for both CCL and NC backends)\n",
     "\n",
     "# rho = m.compute_3d_density(r3d, mdelta=cluster_mass, cdelta=cluster_concentration,\n",
     "#                            z_cl=z_cl, cosmo=cosmo, halo_profile_model='einasto',\n",
@@ -469,13 +471,64 @@
     "\n",
     "plot_profile(r3d, rho, \"$\\\\rho_{\\\\rm 3d}$\")"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "For CCL versions >= 2.8.1.dev73+g86125b08, the surface mass density profile can be calculated with quad_vec numerial integration in addition to the default FFTLog. This option will increase the precision of the profile at large radii and can be enabled by passing `use_projected_quad` keyword argument to `compute_surface_density`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# use quad_vec\n",
+    "Sigma_quad = m.compute_surface_density(\n",
+    "    r3d,\n",
+    "    mdelta=cluster_mass,\n",
+    "    cdelta=cluster_concentration,\n",
+    "    z_cl=z_cl,\n",
+    "    cosmo=cosmo,\n",
+    "    halo_profile_model=\"einasto\",\n",
+    "    alpha_ein=0.17,\n",
+    "    use_projected_quad=True, # use quad_vec\n",
+    "    verbose=True,\n",
+    ")\n",
+    "\n",
+    "plot_profile(r3d, Sigma_quad, \"$\\\\Sigma_{\\\\rm quad}$\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# default behavior\n",
+    "Sigma_FFTLog = m.compute_surface_density(\n",
+    "    r3d,\n",
+    "    mdelta=cluster_mass,\n",
+    "    cdelta=cluster_concentration,\n",
+    "    z_cl=z_cl,\n",
+    "    cosmo=cosmo,\n",
+    "    halo_profile_model=\"einasto\",\n",
+    "    alpha_ein=0.17,\n",
+    "    use_projected_quad=False, # default\n",
+    "    verbose=True,\n",
+    ")\n",
+    "\n",
+    "plot_profile(r3d, Sigma_FFTLog, \"$\\\\Sigma_{\\\\rm FFTLog}$\")"
+   ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "wrk",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
-   "name": "wrk"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -487,7 +540,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.9"
+   "version": "3.11.5"
   }
  },
  "nbformat": 4,
diff --git a/examples/demo_theory_functionality_oo.ipynb b/examples/demo_theory_functionality_oo.ipynb
index 322718713..290e58ae3 100644
--- a/examples/demo_theory_functionality_oo.ipynb
+++ b/examples/demo_theory_functionality_oo.ipynb
@@ -302,19 +302,48 @@
     "plot_profile(r3d, rho, \"$\\\\rho_{\\\\rm 3d}$\")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "For CCL versions >= 2.8.1.dev73+g86125b08, the surface mass density profile can be calculated with quad_vec numerial integration in addition to the default FFTLog. This option will increase the precision of the profile at large radii and can be enabled by calling `set_projected_quad(True)`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# use quad_vec\n",
+    "moo_ein.set_projected_quad(True)\n",
+    "\n",
+    "Sigma_quad = moo_ein.eval_surface_density(r3d, z_cl, verbose=True)\n",
+    "\n",
+    "plot_profile(r3d, Sigma_quad, \"$\\\\Sigma_{\\\\rm quad}$\")"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "# revert the effect from the previous cell\n",
+    "moo_ein.set_projected_quad(False)\n",
+    "\n",
+    "# default behavior\n",
+    "Sigma_FFTLog = moo_ein.eval_surface_density(r3d, z_cl, verbose=True)\n",
+    "\n",
+    "plot_profile(r3d, Sigma_FFTLog, \"$\\\\Sigma_{\\\\rm FFTLog}$\")"
+   ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "wrk",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
-   "name": "wrk"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -326,7 +355,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.9"
+   "version": "3.11.5"
   }
  },
  "nbformat": 4,