I added a function sliderInput into the following code to define a range for the smooth parameter to read this function 
after_tilde <- paste0("ps(", dep_vars, ", lambda = seq(lower,upper,l=20))")
in order to do that I define
lower <- input$range[1]
upper <- input$range[2]
in reactive and renderPrint sections But I have an error and I donot know where I made a mistake in ui section or server section. I used 
       sliderInput("range", "Smooth Parameter range:",min = 0, max = 1000, value = c(0,1000))) to defind the range. I have this error object 'lower' not found. Any advice?
library(shiny)
library(quantreg)
library(quantregGrowth)
ui = tagList(
  tags$head(tags$style(HTML("body{ background: aliceblue; }"))),
  navbarPage(title="",
             tabPanel("Data Import",
                      sidebarLayout(sidebarPanel( fileInput("file","Upload your CSV",multiple = FALSE),
                                                  tags$hr(),
                                                  h5(helpText("Select the read.table parameters below")),
                                                  checkboxInput(inputId = 'header', label = 'Header', value = FALSE),
                                                  checkboxInput(inputId = "stringAsFactors", "StringAsFactors", FALSE),
                                                  radioButtons(inputId = 'sep', label = 'Separator', 
                                                               choices = c(Comma=',',Semicolon=';',Tab='\t', Space=''), selected = ',')
                      ),
                      mainPanel(uiOutput("tb1"))
                      ) ),
             tabPanel("95% Continious Reference Intervals",
                      sidebarLayout(sidebarPanel(
                        uiOutput("model_select"),
                        uiOutput("var1_select"),
                        uiOutput("rest_var_select"),                        
           sliderInput("range", "Smooth Parameter range:",min = 0, max = 1000, value = c(0,1000))
                                                ),
                        mainPanel( helpText("Selected variables and Fitted values"),
                                   verbatimTextOutput("other_val_show")))),
             tabPanel("Model Summary", verbatimTextOutput("summary")), 
             tabPanel("Scatterplot", plotOutput("scatterplot"))#, # Plot             
             ,inverse = TRUE,position="static-top",theme ="bootstrap.css"))
server<-function(input,output) { data <- reactive({
  lower <- input$range[1]
  upper <- input$range[2]
  file1 <- input$file
  if(is.null(file1)){return()} 
  read.table(file=file1$datapath, sep=input$sep, header = input$header, stringsAsFactors = input$stringAsFactors)
})  
output$table <- renderTable({
  if(is.null(data())){return ()}
  data()
})
output$tb1 <- renderUI({
  tableOutput("table")
})
#output$model_select<-renderUI({
#selectInput("modelselect","Select Algo",choices = c("Reference Interval"="Model")) #Logistic_reg
#})
output$var1_select<-renderUI({
  selectInput("ind_var_select","Select Independent Variable", choices =as.list(names(data())),multiple = FALSE)
})
output$rest_var_select<-renderUI({
  checkboxGroupInput("other_var_select","Select Dependent Variable",choices =as.list(names(data()))) #Select other Var
})
output$other_val_show<-renderPrint({
   lower <- input$range[1]
  upper <- input$range[2]
  input$other_var_select
  input$ind_var_select
  f<-data()
  library(caret)
  library(quantregGrowth)
  dep_vars    <- paste0(input$ind_var_select, collapse = "+")
  after_tilde <- paste0("ps(", dep_vars, ", lambda = seq(lower,upper,l=20))")
  dyn_string  <- paste0(input$other_var_select, " ~ ", after_tilde)
  Model<-quantregGrowth::gcrq(as.formula(dyn_string),tau=c(0.025,0.975), data=f)
  temp <- data.frame(Model$fitted)
  growthData_b <- cbind(f, temp)
  print(growthData_b)
})
}
shinyApp(ui=ui,server=server)
 
     
    