Update app.py

app.py

@@ -68,22 +68,27 @@ st.markdown(
     .stButton {
         margin-top: 10px;
     }
+    /* Reduced Padding at the top */
     .css-1d391kg {
         padding-top: 0.5rem;
     }
+    /* Centering the legend in the plot */
     .stPlotlyChart {
         display: block;
         margin: 0 auto;
     }
+    /* Adjusting for full width without scrolling */
     .css-1lcbvhc {
         padding-left: 0;
         padding-right: 0;
     }
+    /* Custom borders for input fields */
     .stTextInput input, .stNumberInput input {
         border: 2px solid #001A6E;
         border-radius: 5px;
         padding: 10px;
     }
+    /* Tooltip styling */
     .tooltip {
         position: relative;
         display: inline-block;
@@ -100,7 +105,7 @@ st.markdown(
         padding: 5px;
         position: absolute;
         z-index: 1;
-        bottom: 125%;
+        bottom: 125%; /* Position the tooltip above */
         left: 50%;
         margin-left: -150px;
         transition: opacity 0.3s;
@@ -129,8 +134,11 @@ with col1:
             <label for="func_input">Enter a function of 'x':</label>
             <span class="tooltiptext">
                 **How to input your function:**
-                - Use `x**n` for powers of x
-                - Use `np.sin(x)`, `np.log(x)`, or `np.exp(x)` for trigonometric, logarithmic, or exponential functions.
+                - Please give the inputs as mentioned below                
+                - x^n as  x**n,                
+                - sin(x) as np.sin(x)                
+                - log(x) as np.log(x),                
+                - e^x or exp(x) as np.exp(x).
             </span>
         </div>
         """,
@@ -152,17 +160,15 @@ with col1:
         key="starting_point", 
         on_change=reset_state
     )
-    learning_rate = st.number_input(
+    new_learning_rate = st.number_input(
         "Learning Rate (ŋ)", 
         value=st.session_state.learning_rate, 
         step=0.01, 
-        format="%.2f", 
-        key="new_learning_rate"
+        format="%.2f"
     )
-
-    # Update learning rate without resetting the state
-    if learning_rate != st.session_state.learning_rate:
-        st.session_state.learning_rate = learning_rate
+    # Update the learning rate without resetting progress
+    if new_learning_rate != st.session_state.learning_rate:
+        st.session_state.learning_rate = new_learning_rate
 
     col3, col4 = st.columns(2)
     with col3: